Untouchable numbers: Difference between revisions

=={{header|Nim}}==

I borrowed some ideas from Go version, but keep the limit to 100_000 as in Wren version.

<lang Nim>import math, strutils

const

Lim1 = 100_000 # Limit for untouchable numbers.

Lim2 = 14 * Lim1 # Limit for computation of sum of divisors.

proc sumdiv(n: uint): uint =

## Return the sum of the strict divisors of "n".

result = 1

let r = sqrt(n.float).uint

let k = if (n and 1) == 0: 1u else: 2u

for d in countup(k + 1, r, k):

if n mod d == 0:

result += d

let q = n div d

if q != d: result += q

var

isSumDiv: array[1..Lim2, bool]

isPrime: array[1..Lim1, bool]

# Fill both sieves in a single pass.

for n in 1u..Lim2:

let s = sumdiv(n)

if s <= Lim2:

isSumDiv[s] = true

if s == 1 and n <= Lim1:

isPrime[n] = true

isPrime[1] = false

# Build list of untouchable numbers.

var list = @[2, 5]

for n in countup(6, Lim1, 2):

if not (isSumDiv[n] or isPrime[n - 1] or isPrime[n - 3]):

list.add n

echo "Untouchable numbers ≤ 2000:"

var count, lcount = 0

for n in list:

if n <= 2000:

stdout.write ($n).align(5)

inc count

inc lcount

if lcount == 20:

echo()

lcount = 0

else:

if lcount > 0: echo()

break

const CountMessage = "There are $1 untouchable numbers ≤ $2."

echo CountMessage.format(count, 2000), '\n'

count = 0

var lim = 10

for n in list:

if n > lim:

echo CountMessage.format(count, lim)

lim *= 10

inc count

if lim == Lim1:

# Emit last message.

echo CountMessage.format(count, lim)</lang>

{{out}}

<pre>Untouchable numbers ≤ 2000:

2 5 52 88 96 120 124 146 162 188 206 210 216 238 246 248 262 268 276 288

290 292 304 306 322 324 326 336 342 372 406 408 426 430 448 472 474 498 516 518

520 530 540 552 556 562 576 584 612 624 626 628 658 668 670 708 714 718 726 732

738 748 750 756 766 768 782 784 792 802 804 818 836 848 852 872 892 894 896 898

902 926 934 936 964 966 976 982 996 1002 1028 1044 1046 1060 1068 1074 1078 1080 1102 1116

1128 1134 1146 1148 1150 1160 1162 1168 1180 1186 1192 1200 1212 1222 1236 1246 1248 1254 1256 1258

1266 1272 1288 1296 1312 1314 1316 1318 1326 1332 1342 1346 1348 1360 1380 1388 1398 1404 1406 1418

1420 1422 1438 1476 1506 1508 1510 1522 1528 1538 1542 1566 1578 1588 1596 1632 1642 1650 1680 1682

1692 1716 1718 1728 1732 1746 1758 1766 1774 1776 1806 1816 1820 1822 1830 1838 1840 1842 1844 1852

1860 1866 1884 1888 1894 1896 1920 1922 1944 1956 1958 1960 1962 1972 1986 1992

There are 196 untouchable numbers ≤ 2000.

There are 2 untouchable numbers ≤ 10.

There are 5 untouchable numbers ≤ 100.

There are 89 untouchable numbers ≤ 1000.

There are 1212 untouchable numbers ≤ 10000.

There are 13863 untouchable numbers ≤ 100000.</pre>