Factor-perfect numbers: Difference between revisions
Created Nim solution.
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OEIS A163272:
0, 1, 48, 1280, 2496, 28672, 29808, 454656, 2342912,
</pre>
=={{header|Nim}}==
{{trans|Python}}
<syntaxhighlight lang="Nim">import std/[algorithm, strutils, sugar, tables]
func moreMultiples(toSeq, fromSeq: seq[int]): seq[seq[int]] =
## Uses the first definition and recursion to generate the sequences.
result = collect:
for i in fromSeq:
if i > toSeq[^1] and i mod toSeq[^1] == 0:
toSeq & i
for i in 0..result.high:
for arr in moreMultiples(result[i], fromSeq):
result.add arr
func divisors(n: int): seq[int] =
## Return the list of divisors of "n".
var d = 1
while d * d <= n:
if n mod d == 0:
let q = n div d
result.add d
if q != d:
result.add q
inc d
result.sort()
func cmp(x, y: seq[int]): int =
## Compare two sequences.
for i in 0..<min(x.len, y.len):
result = cmp(x[i], y[i])
if result != 0: return
result = cmp(x.len, y.len)
let listing = collect(
for a in sorted(moreMultiples(@[1], divisors(48)[1..^2]), cmp):
a & 48) & @[@[1, 48]]
echo "48 sequences using first definition:"
for i, s in listing:
let item = '[' & s.join(", ") & ']'
stdout.write alignLeft(item, 22)
stdout.write if i mod 4 == 3: '\n' else: ' '
# Derive second definition's sequences
echo "\n48 sequences using second definition:"
for i, s1 in listing:
let s2 = collect:
for j in 1..s1.high:
s1[j] div s1[j - 1]
let item = '[' & s2.join(", ") & ']'
stdout.write alignLeft(item, 20)
stdout.write if i mod 4 == 3: '\n' else: ' '
var cache: Table[int, int]
proc erdosFactorCount(n: int): int =
## Erdos method.
if n in cache: return cache[n]
let ds = divisors(n)
if ds.len >= 2:
for d in ds[1..^2]:
result += erdosFactorCount(n div d)
inc result
cache[n] = result
stdout.write "\nOEIS A163272: "
let s = collect:
for num in 0..<2_400_000:
if num == 0 or erdosFactorCount(num) == num:
num
echo s.join(", ")
</syntaxhighlight>
{{out}}
<pre>48 sequences using first definition:
[1, 2, 48] [1, 2, 4, 48] [1, 2, 4, 8, 48] [1, 2, 4, 8, 16, 48]
[1, 2, 4, 8, 24, 48] [1, 2, 4, 12, 48] [1, 2, 4, 12, 24, 48] [1, 2, 4, 16, 48]
[1, 2, 4, 24, 48] [1, 2, 6, 48] [1, 2, 6, 12, 48] [1, 2, 6, 12, 24, 48]
[1, 2, 6, 24, 48] [1, 2, 8, 48] [1, 2, 8, 16, 48] [1, 2, 8, 24, 48]
[1, 2, 12, 48] [1, 2, 12, 24, 48] [1, 2, 16, 48] [1, 2, 24, 48]
[1, 3, 48] [1, 3, 6, 48] [1, 3, 6, 12, 48] [1, 3, 6, 12, 24, 48]
[1, 3, 6, 24, 48] [1, 3, 12, 48] [1, 3, 12, 24, 48] [1, 3, 24, 48]
[1, 4, 48] [1, 4, 8, 48] [1, 4, 8, 16, 48] [1, 4, 8, 24, 48]
[1, 4, 12, 48] [1, 4, 12, 24, 48] [1, 4, 16, 48] [1, 4, 24, 48]
[1, 6, 48] [1, 6, 12, 48] [1, 6, 12, 24, 48] [1, 6, 24, 48]
[1, 8, 48] [1, 8, 16, 48] [1, 8, 24, 48] [1, 12, 48]
[1, 12, 24, 48] [1, 16, 48] [1, 24, 48] [1, 48]
48 sequences using second definition:
[2, 24] [2, 2, 12] [2, 2, 2, 6] [2, 2, 2, 2, 3]
[2, 2, 2, 3, 2] [2, 2, 3, 4] [2, 2, 3, 2, 2] [2, 2, 4, 3]
[2, 2, 6, 2] [2, 3, 8] [2, 3, 2, 4] [2, 3, 2, 2, 2]
[2, 3, 4, 2] [2, 4, 6] [2, 4, 2, 3] [2, 4, 3, 2]
[2, 6, 4] [2, 6, 2, 2] [2, 8, 3] [2, 12, 2]
[3, 16] [3, 2, 8] [3, 2, 2, 4] [3, 2, 2, 2, 2]
[3, 2, 4, 2] [3, 4, 4] [3, 4, 2, 2] [3, 8, 2]
[4, 12] [4, 2, 6] [4, 2, 2, 3] [4, 2, 3, 2]
[4, 3, 4] [4, 3, 2, 2] [4, 4, 3] [4, 6, 2]
[6, 8] [6, 2, 4] [6, 2, 2, 2] [6, 4, 2]
[8, 6] [8, 2, 3] [8, 3, 2] [12, 4]
[12, 2, 2] [16, 3] [24, 2] [48]
OEIS A163272: 0, 1, 48, 1280, 2496, 28672, 29808, 454656, 2342912
</pre>
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