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A positive integer n is said to be a Rhonda number to base b if the product of the base b digits of n is equal to b times the sum of n's prime factors.

These numbers were named by Kevin Brown after an acquaintance of his whose residence number was 25662, a member of the base 10 numbers with this property.

25662 is a Rhonda number to base-10. The prime factorization is 2 × 3 × 7 × 13 × 47; the product of its base-10 digits is equal to the base times the sum of its prime factors:

2 × 5 × 6 × 6 × 2 = 720 = 10 × (2 + 3 + 7 + 13 + 47)

Rhonda numbers only exist in bases that are not a prime.

Rhonda numbers to base 10 always contain at least 1 digit 5 and always contain at least 1 even digit.

Task

For the non-prime bases b from 2 through 16 , find and display here, on this page, at least the first 10 Rhonda numbers to base b. Display the found numbers at least in base 10.

Stretch

Extend out to base 36.

See also

Wolfram Mathworld - Rhonda numbers Numbers Aplenty - Rhonda numbers OEIS:A100968 - Integers n that are Rhonda numbers to base 4 OEIS:A100969 - Integers n that are Rhonda numbers to base 6 OEIS:A100970 - Integers n that are Rhonda numbers to base 8 OEIS:A100973 - Integers n that are Rhonda numbers to base 9 OEIS:A099542 - Rhonda numbers to base 10 OEIS:A100971 - Integers n that are Rhonda numbers to base 12 OEIS:A100972 - Integers n that are Rhonda numbers to base 14 OEIS:A100974 - Integers n that are Rhonda numbers to base 15 OEIS:A100975 - Integers n that are Rhonda numbers to base 16

OEIS:A255735 - Integers n that are Rhonda numbers to base 18 OEIS:A255732 - Rhonda numbers in vigesimal number system (base 20) OEIS:A255736 - Integers that are Rhonda numbers to base 30

Related Task: Smith numbers

Julia

<lang julia>using Primes

isRhonda(n, b) = prod(digits(n, base=b)) == b * sum([prod(pair) for pair in factor(n).pe])

function displayrhondas(low, high, nshow)

   for b in filter(!isprime, low:high)
       n, rhondas = 1, Int[]
       while length(rhondas) < nshow
           isRhonda(n, b) && push!(rhondas, n)
           n += 1
       end
       println("First $nshow Rhondas in base $b:")
       println("In base 10: ", rhondas)
       println("In base $b: ", replace(string([string(i, base=b) for i in rhondas]), "\"" => ""), "\n")
   end

end

displayrhondas(2, 16, 15)

</lang>

Output:

First 15 Rhondas in base 4:
In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902]
In base 4: [2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221, 333122221, 1123133332, 1133232321, 1322333131, 2132222232]

First 15 Rhondas in base 6:
In base 10: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821]
In base 6: [3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132, 513543, 522253, 1143252, 1223224, 1241553]

First 15 Rhondas in base 8:
In base 10: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429]
In base 8: [3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544, 73542, 114457, 114635, 143273, 144345]

First 15 Rhondas in base 9:
In base 10: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944]
In base 9: [23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376, 126733, 136273, 136723, 156264, 158316]

First 15 Rhondas in base 10:
In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662]
In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662]

First 15 Rhondas in base 12:
In base 10: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264]
In base 12: [3a8, 568, 2389, 2689, 27b6, 29b4, 4297, 4974, 5483, 6a35, 6b64, 7662, 86b8, 8864, 94b4]

First 15 Rhondas in base 14:
In base 10: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543]
In base 14: [4279, 6b27, 76cd, ab27, b7c1, 1277d, 173da, 17547, 17bc2, 19437, 1a873, 1b17a, 25377, 28427, 33a75]

First 15 Rhondas in base 15:
In base 10: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483]
In base 15: [a97, aec, 35e8, 4a83, 5269, 5586, 5a1c, 5e39, 735d, 91a8, 936a, 9ba4, 9e1a, b385, ba73]

First 15 Rhondas in base 16:
In base 10: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465]
In base 16: [3e8, 46e, 1a78, 3e28, 4ca8, 4e4b, 4f83, 5d8a, 66b8, 718e, 7ca2, 7e24, 85bc, 86d9, 8e71]

Phix

with javascript_semantics
constant fmt = """
First 15 Rhonda numbers in base %d:
In base 10:  %s
In base %-2d:  %s

"""
function digit(integer d) return d-iff(d<='9'?'0':'a'-10) end function

for base=2 to 36 do
    if not is_prime(base) then
        sequence rhondab = {},  -- (base)
                 rhondad = {}   -- (decimal)
        integer n = 1
        while length(rhondab)<15 do
            string digits = sprintf("%a",{{base,n}})
            if not find('0',digits)
            and (base!=10 or (find('5',digits) and sum(apply(digits,even))!=0)) then
                integer pd = product(apply(digits,digit)),
                        bs = base*sum(prime_factors(n,true,-1))
                if pd==bs then
                    string decdig = sprintf("%d",n)
                    integer l = max(length(decdig),length(digits))
                    rhondab = append(rhondab,pad_head(digits,l))
                    rhondad = append(rhondad,pad_head(decdig,l))
                end if
            end if
            n += 1
        end while
        printf(1,fmt,{base,join(rhondad),base,join(rhondab)})
    end if
end for

Output:

First 15 Rhonda numbers in base 4:
In base 10:    10206   11935   12150   16031    45030     94185    113022    114415    191149    244713    259753     374782     392121     503773     649902
In base 4 :  2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhonda numbers in base 6:
In base 10:   855 1029  3813  5577  7040  7304  15104  19136  35350  36992  41031  42009   60368   65536   67821
In base 6 :  3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhonda numbers in base 8:
In base 10:  1836  6318  6622 10530 14500 14739 17655 18550 25398 25956 30562  39215  39325  50875  51429
In base 8 :  3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhonda numbers in base 9:
In base 10:  15540 21054 25331 44360 44660 44733 47652 50560 54944  76857  77142  83334  83694  96448  97944
In base 9 :  23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhonda numbers in base 10:
In base 10:  1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10:  1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers in base 12:
In base 10:  560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12:  3a8 568 2389 2689 27b6 29b4 4297 4974 5483  6a35  6b64  7662  86b8  8864  94b4

First 15 Rhonda numbers in base 14:
In base 10:  11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14:   4279  6b27  76cd  ab27  b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427  33a75

First 15 Rhonda numbers in base 15:
In base 10:  2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15:   a97  aec  35e8  4a83  5269  5586  5a1c  5e39  735d  91a8  936a  9ba4  9e1a  b385  ba73

First 15 Rhonda numbers in base 16:
In base 10:  1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16:   3e8  46e 1a78  3e28  4ca8  4e4b  4f83  5d8a  66b8  718e  7ca2  7e24  85bc  86d9  8e71

First 15 Rhonda numbers in base 18:
In base 10:  1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18:   49c  94c 1998  2g9f  35fg  39d4  3b36  3e6g  49f8  64e9  6a6e  77a9  7g19  8696  956d

First 15 Rhonda numbers in base 20:
In base 10:  1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20:   4af  17ca  1i4f  2ci5  2f85  3gf2  465a  46c5  55ec  5a85  6a2j  6dag  84h5  9g1a  a1fc

First 15 Rhonda numbers in base 21:
In base 10:  1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21:   3ef  c4e  j67  189e  1ebc  2eg6  33ec  3e2i  45e9  55i7  5697  6d3e  93j7  9e34  9j37

First 15 Rhonda numbers in base 22:
In base 10:  2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22:   5cb  8be  g5b  2fb2  2lb8  3ab4  6gb1  6lbc   b16g   b1cj   b96a   bi78   c7bl   g9fb   i25b

First 15 Rhonda numbers in base 24:
In base 10:  2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24:   3eg  4gl  6lg  9ic  9jg  c9g  e9g  fg6   hce  16dk  1bgf  1ihg  1lcg  22ci  26ei

First 15 Rhonda numbers in base 25:
In base 10:  6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25:   ake  fa8   l5a  1a5m  3aa7  3h5f  45ff  4aa6  655e   8o55   93f5   95ja   a5do   aa2f   aek4

First 15 Rhonda numbers in base 26:
In base 10:  7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26:   bde  dke  dme   gd6  16kd  1f6d  1pgd  2e6d  2i2d  2kmd  3ecd  43ed  45kd   64md   7die

First 15 Rhonda numbers in base 27:
In base 10:  4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27:   6fi   g6i   gf9   i2o   k9i   o9b  169k  19ni  1aii  29jf  2i9j  2q9i  32ig  337l  339l

First 15 Rhonda numbers in base 28:
In base 10:  3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28:   3qe  7bc  7c8  9ee   e6g   hc7  16lq  17qq  18em  1m67  1mce  273o  28oe  2al6  2bei

First 15 Rhonda numbers in base 30:
In base 10:  3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30:   3ao  3fi  5kf  5s6  6ia  7fc  8ia  8p6  9ca  afq  aj6  as9   bfa   cn5   eef

First 15 Rhonda numbers in base 32:
In base 10:  1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32:   1so  3gg   d6g   fg4   gas   geh   oq2   p4o   s8n  1ebg  1gea  1hoo  1s4s  1vc8  288l

First 15 Rhonda numbers in base 33:
In base 10:  756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33:   mu  6fb  6vb   cmw   mtf   s3m  1lgb  1pbu  1q3m   3lml   6b78   7bfb   8o2b   9btg   9jm8

First 15 Rhonda numbers in base 34:
In base 10:  5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34:   4uh   c8h   dhe   e8h   j6h   w4h   36lh   3ehi   3f4h   3hqo   3jeh   4h6e   6csh   6h28   7hoi

First 15 Rhonda numbers in base 35:
In base 10:  8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35:   6p7  7pq  7u8   f7e   p9e   y7a  17lu  17sa  1bfe  1fl7  1fpl  1j5e  2a7f   2def   2ebk

First 15 Rhonda numbers in base 36:
In base 10:  1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36:    rs  3pc  4di  6bi   8hi   9ks   a9g   c5i   cz9   hrc  13to  14ou  1g9s  1iq9  1lw6

Raku

Find and show the first 15 so as to display the namesake Rhonda number 25662. <lang perl6>use Prime::Factor;

my @factor-sum;

@factor-sum[1000000] = 42; # Sink a large index to make access thread safe

sub rhonda ($base) {

   (1..∞).hyper.map: { $_ if $base * (@factor-sum[$_] //= .&prime-factors.sum) == [×] .polymod($base xx *) }

}

for (flat 2..16, 17..36).grep: { !.&is-prime } -> $b {

   put "\nFirst 15 Rhonda numbers to base $b:";
   my @rhonda = rhonda($b)[^15];
   my $ch = @rhonda[*-1].chars max @rhonda[*-1].base($b).chars;
   put "In base 10: " ~ @rhonda».fmt("%{$ch}s").join: ', ';
   put $b.fmt("In base %2d: ") ~ @rhonda».base($b)».fmt("%{$ch}s").join: ', ';

}</lang>

Output:

First 15 Rhonda numbers to base 4:
In base 10:      10206,      11935,      12150,      16031,      45030,      94185,     113022,     114415,     191149,     244713,     259753,     374782,     392121,     503773,     649902
In base  4:    2133132,    2322133,    2331312,    3322133,   22333212,  112333221,  123211332,  123323233,  232222231,  323233221,  333122221, 1123133332, 1133232321, 1322333131, 2132222232

First 15 Rhonda numbers to base 6:
In base 10:     855,    1029,    3813,    5577,    7040,    7304,   15104,   19136,   35350,   36992,   41031,   42009,   60368,   65536,   67821
In base  6:    3543,    4433,   25353,   41453,   52332,   53452,  153532,  224332,  431354,  443132,  513543,  522253, 1143252, 1223224, 1241553

First 15 Rhonda numbers to base 8:
In base 10:   1836,   6318,   6622,  10530,  14500,  14739,  17655,  18550,  25398,  25956,  30562,  39215,  39325,  50875,  51429
In base  8:   3454,  14256,  14736,  24442,  34244,  34623,  42367,  44166,  61466,  62544,  73542, 114457, 114635, 143273, 144345

First 15 Rhonda numbers to base 9:
In base 10:  15540,  21054,  25331,  44360,  44660,  44733,  47652,  50560,  54944,  76857,  77142,  83334,  83694,  96448,  97944
In base  9:  23276,  31783,  37665,  66758,  67232,  67323,  72326,  76317,  83328, 126376, 126733, 136273, 136723, 156264, 158316

First 15 Rhonda numbers to base 10:
In base 10:  1568,  2835,  4752,  5265,  5439,  5664,  5824,  5832,  8526, 12985, 15625, 15698, 19435, 25284, 25662
In base 10:  1568,  2835,  4752,  5265,  5439,  5664,  5824,  5832,  8526, 12985, 15625, 15698, 19435, 25284, 25662

First 15 Rhonda numbers to base 12:
In base 10:   560,   800,  3993,  4425,  4602,  4888,  7315,  8296,  9315, 11849, 12028, 13034, 14828, 15052, 16264
In base 12:   3A8,   568,  2389,  2689,  27B6,  29B4,  4297,  4974,  5483,  6A35,  6B64,  7662,  86B8,  8864,  94B4

First 15 Rhonda numbers to base 14:
In base 10:  11475,  18655,  20565,  29631,  31725,  45387,  58404,  58667,  59950,  63945,  67525,  68904,  91245,  99603, 125543
In base 14:   4279,   6B27,   76CD,   AB27,   B7C1,  1277D,  173DA,  17547,  17BC2,  19437,  1A873,  1B17A,  25377,  28427,  33A75

First 15 Rhonda numbers to base 15:
In base 10:  2392,  2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483
In base 15:   A97,   AEC,  35E8,  4A83,  5269,  5586,  5A1C,  5E39,  735D,  91A8,  936A,  9BA4,  9E1A,  B385,  BA73

First 15 Rhonda numbers to base 16:
In base 10:  1000,  1134,  6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465
In base 16:   3E8,   46E,  1A78,  3E28,  4CA8,  4E4B,  4F83,  5D8A,  66B8,  718E,  7CA2,  7E24,  85BC,  86D9,  8E71

First 15 Rhonda numbers to base 18:
In base 10:  1470,  3000,  8918, 17025, 19402, 20650, 21120, 22156, 26522, 36549, 38354, 43281, 46035, 48768, 54229
In base 18:   49C,   94C,  1998,  2G9F,  35FG,  39D4,  3B36,  3E6G,  49F8,  64E9,  6A6E,  77A9,  7G19,  8696,  956D

First 15 Rhonda numbers to base 20:
In base 10:  1815, 11050, 15295, 21165, 22165, 30702, 34510, 34645, 42292, 44165, 52059, 53416, 65945, 78430, 80712
In base 20:   4AF,  17CA,  1I4F,  2CI5,  2F85,  3GF2,  465A,  46C5,  55EC,  5A85,  6A2J,  6DAG,  84H5,  9G1A,  A1FC

First 15 Rhonda numbers to base 21:
In base 10:  1632,  5390,  8512, 12992, 15678, 25038, 29412, 34017, 39552, 48895, 49147, 61376, 85078, 89590, 91798
In base 21:   3EF,   C4E,   J67,  189E,  1EBC,  2EG6,  33EC,  3E2I,  45E9,  55I7,  5697,  6D3E,  93J7,  9E34,  9J37

First 15 Rhonda numbers to base 22:
In base 10:   2695,   4128,   7865,  28800,  31710,  37030,  71875,  74306, 117760, 117895, 121626, 126002, 131427, 175065, 192753
In base 22:    5CB,    8BE,    G5B,   2FB2,   2LB8,   3AB4,   6GB1,   6LBC,   B16G,   B1CJ,   B96A,   BI78,   C7BL,   G9FB,   I25B

First 15 Rhonda numbers to base 24:
In base 10:  2080,  2709,  3976,  5628,  5656,  7144,  8296,  9030, 10094, 17612, 20559, 24616, 26224, 29106, 31458
In base 24:   3EG,   4GL,   6LG,   9IC,   9JG,   C9G,   E9G,   FG6,   HCE,  16DK,  1BGF,  1IHG,  1LCG,  22CI,  26EI

First 15 Rhonda numbers to base 25:
In base 10:   6764,   9633,  13260,  22022,  53382,  57640,  66015,  69006,  97014, 140130, 142880, 144235, 159724, 162565, 165504
In base 25:    AKE,    FA8,    L5A,   1A5M,   3AA7,   3H5F,   45FF,   4AA6,   655E,   8O55,   93F5,   95JA,   A5DO,   AA2F,   AEK4

First 15 Rhonda numbers to base 26:
In base 10:   7788,   9322,   9374,  11160,  22165,  27885,  34905,  44785,  47385,  49257,  62517,  72709,  74217, 108745, 132302
In base 26:    BDE,    DKE,    DME,    GD6,   16KD,   1F6D,   1PGD,   2E6D,   2I2D,   2KMD,   3ECD,   43ED,   45KD,   64MD,   7DIE

First 15 Rhonda numbers to base 27:
In base 10:  4797, 11844, 12078, 13200, 14841, 17750, 24320, 26883, 27477, 46455, 52750, 58581, 61009, 61446, 61500
In base 27:   6FI,   G6I,   GF9,   I2O,   K9I,   O9B,  169K,  19NI,  1AII,  29JF,  2I9J,  2Q9I,  32IG,  337L,  339L

First 15 Rhonda numbers to base 28:
In base 10:  3094,  5808,  5832,  7462, 11160, 13671, 27270, 28194, 28638, 39375, 39550, 49500, 50862, 52338, 52938
In base 28:   3QE,   7BC,   7C8,   9EE,   E6G,   HC7,  16LQ,  17QQ,  18EM,  1M67,  1MCE,  273O,  28OE,  2AL6,  2BEI

First 15 Rhonda numbers to base 30:
In base 10:  3024,  3168,  5115,  5346,  5950,  6762,  7750,  7956,  8470,  9476,  9576,  9849, 10360, 11495, 13035
In base 30:   3AO,   3FI,   5KF,   5S6,   6IA,   7FC,   8IA,   8P6,   9CA,   AFQ,   AJ6,   AS9,   BFA,   CN5,   EEF

First 15 Rhonda numbers to base 32:
In base 10:  1944,  3600, 13520, 15876, 16732, 16849, 25410, 25752, 28951, 47472, 49610, 50968, 61596, 64904, 74005
In base 32:   1SO,   3GG,   D6G,   FG4,   GAS,   GEH,   OQ2,   P4O,   S8N,  1EBG,  1GEA,  1HOO,  1S4S,  1VC8,  288L

First 15 Rhonda numbers to base 33:
In base 10:    756,   7040,   7568,  13826,  24930,  30613,  59345,  63555,  64372, 131427, 227840, 264044, 313709, 336385, 344858
In base 33:     MU,    6FB,    6VB,    CMW,    MTF,    S3M,   1LGB,   1PBU,   1Q3M,   3LML,   6B78,   7BFB,   8O2B,   9BTG,   9JM8

First 15 Rhonda numbers to base 34:
In base 10:   5661,  14161,  15620,  16473,  22185,  37145, 125579, 134692, 135405, 138472, 140369, 177086, 250665, 255552, 295614
In base 34:    4UH,    C8H,    DHE,    E8H,    J6H,    W4H,   36LH,   3EHI,   3F4H,   3HQO,   3JEH,   4H6E,   6CSH,   6H28,   7HOI

First 15 Rhonda numbers to base 35:
In base 10:   8232,   9476,   9633,  18634,  30954,  41905,  52215,  52440,  56889,  61992,  62146,  66339,  98260, 102180, 103305
In base 35:    6P7,    7PQ,    7U8,    F7E,    P9E,    Y7A,   17LU,   17SA,   1BFE,   1FL7,   1FPL,   1J5E,   2A7F,   2DEF,   2EBK

First 15 Rhonda numbers to base 36:
In base 10:  1000,  4800,  5670,  8190, 10998, 12412, 13300, 15750, 16821, 23016, 51612, 52734, 67744, 70929, 75030
In base 36:    RS,   3PC,   4DI,   6BI,   8HI,   9KS,   A9G,   C5I,   CZ9,   HRC,  13TO,  14OU,  1G9S,  1IQ9,  1LW6

Wren

Library: Wren-math

Library: Wren-fmt

<lang ecmascript>import "./math" for Math, Int, Nums import "./fmt" for Fmt, Conv

for (b in 2..36) {

   if (Int.isPrime(b)) continue
   var count = 0
   var rhonda = []
   var n = 1
   while (count < 15) {
       var digits = Int.digits(n, b)
       if (!digits.contains(0)) {
           if (b != 10 || (digits.contains(5) && digits.any { |d| d % 2 == 0 })) {
               var calc1 = Nums.prod(digits)
               var calc2 = b * Nums.sum(Int.primeFactors(n))
               if (calc1 == calc2) {
                   rhonda.add(n)
                   count = count + 1
               }
           }
       }
       n = n + 1
   }
   if (rhonda.count > 0) {
       System.print("\nFirst 15 Rhonda numbers in base %(b):")
       var rhonda2 = rhonda.map { |r| r.toString }.toList
       var rhonda3 = rhonda.map { |r| Conv.Itoa(r, b) }.toList
       var maxLen2 = Nums.max(rhonda2.map { |r| r.count })
       var maxLen3 = Nums.max(rhonda3.map { |r| r.count })
       var maxLen  = Math.max(maxLen2, maxLen3) + 1
       Fmt.print("In base 10:  $*s", maxLen, rhonda2)
       Fmt.print("In base $-2d:  $*s", b, maxLen, rhonda3)
   }

}</lang>

Output:

First 15 Rhonda numbers in base 4:
In base 10:        10206       11935       12150       16031       45030       94185      113022      114415      191149      244713      259753      374782      392121      503773      649902
In base 4 :      2133132     2322133     2331312     3322133    22333212   112333221   123211332   123323233   232222231   323233221   333122221  1123133332  1133232321  1322333131  2132222232

First 15 Rhonda numbers in base 6:
In base 10:       855     1029     3813     5577     7040     7304    15104    19136    35350    36992    41031    42009    60368    65536    67821
In base 6 :      3543     4433    25353    41453    52332    53452   153532   224332   431354   443132   513543   522253  1143252  1223224  1241553

First 15 Rhonda numbers in base 8:
In base 10:     1836    6318    6622   10530   14500   14739   17655   18550   25398   25956   30562   39215   39325   50875   51429
In base 8 :     3454   14256   14736   24442   34244   34623   42367   44166   61466   62544   73542  114457  114635  143273  144345

First 15 Rhonda numbers in base 9:
In base 10:    15540   21054   25331   44360   44660   44733   47652   50560   54944   76857   77142   83334   83694   96448   97944
In base 9 :    23276   31783   37665   66758   67232   67323   72326   76317   83328  126376  126733  136273  136723  156264  158316

First 15 Rhonda numbers in base 10:
In base 10:    1568   2835   4752   5265   5439   5664   5824   5832   8526  12985  15625  15698  19435  25284  25662
In base 10:    1568   2835   4752   5265   5439   5664   5824   5832   8526  12985  15625  15698  19435  25284  25662

First 15 Rhonda numbers in base 12:
In base 10:     560    800   3993   4425   4602   4888   7315   8296   9315  11849  12028  13034  14828  15052  16264
In base 12:     3A8    568   2389   2689   27B6   29B4   4297   4974   5483   6A35   6B64   7662   86B8   8864   94B4

First 15 Rhonda numbers in base 14:
In base 10:    11475   18655   20565   29631   31725   45387   58404   58667   59950   63945   67525   68904   91245   99603  125543
In base 14:     4279    6B27    76CD    AB27    B7C1   1277D   173DA   17547   17BC2   19437   1A873   1B17A   25377   28427   33A75

First 15 Rhonda numbers in base 15:
In base 10:    2392   2472  11468  15873  17424  18126  19152  20079  24388  30758  31150  33004  33550  37925  39483
In base 15:     A97    AEC   35E8   4A83   5269   5586   5A1C   5E39   735D   91A8   936A   9BA4   9E1A   B385   BA73

First 15 Rhonda numbers in base 16:
In base 10:    1000   1134   6776  15912  19624  20043  20355  23946  26296  29070  31906  32292  34236  34521  36465
In base 16:     3E8    46E   1A78   3E28   4CA8   4E4B   4F83   5D8A   66B8   718E   7CA2   7E24   85BC   86D9   8E71

First 15 Rhonda numbers in base 18:
In base 10:    1470   3000   8918  17025  19402  20650  21120  22156  26522  36549  38354  43281  46035  48768  54229
In base 18:     49C    94C   1998   2G9F   35FG   39D4   3B36   3E6G   49F8   64E9   6A6E   77A9   7G19   8696   956D

First 15 Rhonda numbers in base 20:
In base 10:    1815  11050  15295  21165  22165  30702  34510  34645  42292  44165  52059  53416  65945  78430  80712
In base 20:     4AF   17CA   1I4F   2CI5   2F85   3GF2   465A   46C5   55EC   5A85   6A2J   6DAG   84H5   9G1A   A1FC

First 15 Rhonda numbers in base 21:
In base 10:    1632   5390   8512  12992  15678  25038  29412  34017  39552  48895  49147  61376  85078  89590  91798
In base 21:     3EF    C4E    J67   189E   1EBC   2EG6   33EC   3E2I   45E9   55I7   5697   6D3E   93J7   9E34   9J37

First 15 Rhonda numbers in base 22:
In base 10:     2695    4128    7865   28800   31710   37030   71875   74306  117760  117895  121626  126002  131427  175065  192753
In base 22:      5CB     8BE     G5B    2FB2    2LB8    3AB4    6GB1    6LBC    B16G    B1CJ    B96A    BI78    C7BL    G9FB    I25B

First 15 Rhonda numbers in base 24:
In base 10:    2080   2709   3976   5628   5656   7144   8296   9030  10094  17612  20559  24616  26224  29106  31458
In base 24:     3EG    4GL    6LG    9IC    9JG    C9G    E9G    FG6    HCE   16DK   1BGF   1IHG   1LCG   22CI   26EI

First 15 Rhonda numbers in base 25:
In base 10:     6764    9633   13260   22022   53382   57640   66015   69006   97014  140130  142880  144235  159724  162565  165504
In base 25:      AKE     FA8     L5A    1A5M    3AA7    3H5F    45FF    4AA6    655E    8O55    93F5    95JA    A5DO    AA2F    AEK4

First 15 Rhonda numbers in base 26:
In base 10:     7788    9322    9374   11160   22165   27885   34905   44785   47385   49257   62517   72709   74217  108745  132302
In base 26:      BDE     DKE     DME     GD6    16KD    1F6D    1PGD    2E6D    2I2D    2KMD    3ECD    43ED    45KD    64MD    7DIE

First 15 Rhonda numbers in base 27:
In base 10:    4797  11844  12078  13200  14841  17750  24320  26883  27477  46455  52750  58581  61009  61446  61500
In base 27:     6FI    G6I    GF9    I2O    K9I    O9B   169K   19NI   1AII   29JF   2I9J   2Q9I   32IG   337L   339L

First 15 Rhonda numbers in base 28:
In base 10:    3094   5808   5832   7462  11160  13671  27270  28194  28638  39375  39550  49500  50862  52338  52938
In base 28:     3QE    7BC    7C8    9EE    E6G    HC7   16LQ   17QQ   18EM   1M67   1MCE   273O   28OE   2AL6   2BEI

First 15 Rhonda numbers in base 30:
In base 10:    3024   3168   5115   5346   5950   6762   7750   7956   8470   9476   9576   9849  10360  11495  13035
In base 30:     3AO    3FI    5KF    5S6    6IA    7FC    8IA    8P6    9CA    AFQ    AJ6    AS9    BFA    CN5    EEF

First 15 Rhonda numbers in base 32:
In base 10:    1944   3600  13520  15876  16732  16849  25410  25752  28951  47472  49610  50968  61596  64904  74005
In base 32:     1SO    3GG    D6G    FG4    GAS    GEH    OQ2    P4O    S8N   1EBG   1GEA   1HOO   1S4S   1VC8   288L

First 15 Rhonda numbers in base 33:
In base 10:      756    7040    7568   13826   24930   30613   59345   63555   64372  131427  227840  264044  313709  336385  344858
In base 33:       MU     6FB     6VB     CMW     MTF     S3M    1LGB    1PBU    1Q3M    3LML    6B78    7BFB    8O2B    9BTG    9JM8

First 15 Rhonda numbers in base 34:
In base 10:     5661   14161   15620   16473   22185   37145  125579  134692  135405  138472  140369  177086  250665  255552  295614
In base 34:      4UH     C8H     DHE     E8H     J6H     W4H    36LH    3EHI    3F4H    3HQO    3JEH    4H6E    6CSH    6H28    7HOI

First 15 Rhonda numbers in base 35:
In base 10:     8232    9476    9633   18634   30954   41905   52215   52440   56889   61992   62146   66339   98260  102180  103305
In base 35:      6P7     7PQ     7U8     F7E     P9E     Y7A    17LU    17SA    1BFE    1FL7    1FPL    1J5E    2A7F    2DEF    2EBK

First 15 Rhonda numbers in base 36:
In base 10:    1000   4800   5670   8190  10998  12412  13300  15750  16821  23016  51612  52734  67744  70929  75030
In base 36:      RS    3PC    4DI    6BI    8HI    9KS    A9G    C5I    CZ9    HRC   13TO   14OU   1G9S   1IQ9   1LW6