Achilles numbers: Difference between revisions
Nim solution.
Thundergnat (talk | contribs) m (Automated syntax highlighting fixup (second round - minor fixes)) |
(Nim solution.) |
||
Line 2,157:
6 664
7 2242</pre>
=={{header|Nim}}==
{{trans|Wren}}
<syntaxhighlight lang="Nim">import std/[algorithm, sets, math, sequtils, strformat, strutils]
const MaxDigits = 15
func getPerfectPowers(maxExp: int): HashSet[int] =
let upper = 10^maxExp
for i in 2..int(sqrt(upper.toFloat)):
var p = i
while p < upper div i:
p *= i
result.incl p
let pps = getPerfectPowers(MaxDigits)
proc getAchilles(minExp, maxExp: int): HashSet[int] =
let lower = 10^minExp
let upper = 10^maxExp
for b in 1..int(cbrt(upper.toFloat)):
let b3 = b * b * b
for a in 1..int(sqrt(upper.toFloat)):
let p = b3 * a * a
if p >= upper: break
if p >= lower:
if p notin pps: result.incl p
### Part 1 ###
let achillesSet = getAchilles(1, 6)
let achilles = sorted(achillesSet.toSeq)
echo "First 50 Achilles numbers:"
for i in 0..49:
let n = achilles[i]
stdout.write &"{n:>4}"
stdout.write if i mod 10 == 9: '\n' else: ' '
### Part 2 ###
func totient(n: int): int =
var n = n
result = n
var i = 2
while i * i <= n:
if n mod i == 0:
while n mod i == 0:
n = int(n / i)
result -= int(result / i)
if i == 2: i = 1
inc i, 2
if n > 1:
result -= int(result / n)
echo "\nFirst 50 strong Achilles numbers:"
var strongAchilles: seq[int]
var count = 0
for n in achilles:
let tot = totient(n)
if tot in achillesSet:
strongAchilles.add n
inc count
if count == 50: break
for i, n in strongAchilles:
stdout.write &"{n:>6}"
stdout.write if i mod 10 == 9: '\n' else: ' '
### Part 3 ###
echo "\nNumber of Achilles numbers with:"
for d in 2..MaxDigits:
let ac = getAchilles(d - 1, d).len
echo &"{d:>2} digits: {ac}"
</syntaxhighlight>
{{out}}
<pre>First 50 Achilles numbers:
72 108 200 288 392 432 500 648 675 800
864 968 972 1125 1152 1323 1352 1372 1568 1800
1944 2000 2312 2592 2700 2888 3087 3200 3267 3456
3528 3872 3888 4000 4232 4500 4563 4608 5000 5292
5324 5400 5408 5488 6075 6125 6272 6728 6912 7200
First 50 strong Achilles numbers:
500 864 1944 2000 2592 3456 5000 10125 10368 12348
12500 16875 19652 19773 30375 31104 32000 33275 37044 40500
49392 50000 52488 55296 61731 64827 67500 69984 78608 80000
81000 83349 84375 93312 108000 111132 124416 128000 135000 148176
151875 158184 162000 165888 172872 177957 197568 200000 202612 209952
Number of Achilles numbers with:
2 digits: 1
3 digits: 12
4 digits: 47
5 digits: 192
6 digits: 664
7 digits: 2242
8 digits: 7395
9 digits: 24008
10 digits: 77330
11 digits: 247449
12 digits: 788855
13 digits: 2508051
14 digits: 7960336
15 digits: 25235383
</pre>
=={{header|Perl}}==
| |||