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 A145642 Cubefree part of n!. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..500 Rafael Jakimczuk, On the h-th free part of the factorial, International Mathematical Forum, Vol. 12, 2017, no. 13, 629-634. Eric Weisstein's World of Mathematics, Cubefree Part. FORMULA a(n) = A050985(A000142(n)). - Michel Marcus, Nov 07 2013 MATHEMATICA CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[n! ], {n, 1, 40}] PROG (Python) from operator import mul from functools import reduce from sympy import factorint def A145642(n): ....return 1 if n <=1 else reduce(mul, [p**(e % 3) for p, e in factorint(math.factorial(n)).items()]) # Chai Wah Wu, Feb 04 2015 (PARI) a(n) = my(f=factor(n!)); f[, 2] = apply(x->(x % 3), f[, 2]); factorback(f); \\ Michel Marcus, Jan 06 2019 CROSSREFS Cf. A000142 (n!), A050985 (cubefree part). CF. A055204 (squarefree part of n!). Sequence in context: A302033 A337643 A071301 * A056195 A083169 A276817 Adjacent sequences: A145639 A145640 A145641 * A145643 A145644 A145645 KEYWORD nonn AUTHOR Artur Jasinski, Oct 15 2008 STATUS approved

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Last modified June 2 10:58 EDT 2023. Contains 363097 sequences. (Running on oeis4.)