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A145642
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Cubefree part of n!.
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8
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1, 2, 6, 3, 15, 90, 630, 630, 210, 2100, 23100, 34650, 450450, 6306300, 28028, 7007, 119119, 2144142, 40738698, 101846745, 230945, 5080790, 116858170, 350574510, 70114902, 1822987452, 1822987452, 6380456082, 185033226378, 5550996791340
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OFFSET
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1,2
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LINKS
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FORMULA
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log(a(n)) = log(3) * n + o(n) (Jakimczuk, 2017). (End)
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MATHEMATICA
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CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[n! ], {n, 1, 40}]
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PROG
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(Python)
from operator import mul
from functools import reduce
from sympy import factorint
....return 1 if n <=1 else reduce(mul, [p**(e % 3) for p, e in factorint(math.factorial(n)).items()])
(PARI) a(n) = my(f=factor(n!)); f[, 2] = apply(x->(x % 3), f[, 2]); factorback(f); \\ Michel Marcus, Jan 06 2019
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CROSSREFS
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CF. A055204 (squarefree part of n!).
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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