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A069260 a(n) = core(1)*core(2)*...*core(n) where core(x) is the squarefree part of x (see A007913). 0
1, 2, 6, 6, 30, 180, 1260, 2520, 2520, 25200, 277200, 831600, 10810800, 151351200, 2270268000, 2270268000, 38594556000, 77189112000, 1466593128000, 7332965640000, 153992278440000, 3387830125680000, 77920092890640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A "core" analog of n! (A000142) - might be called a "c-factorial" (see formula). - Vladimir Shevelev, Oct 22 2014

LINKS

Table of n, a(n) for n=1..23.

FORMULA

Let p_n = prime(n). a(n) = n!^(c) = p_1^b_1*p_2^b_2*...*p_k^b_k, where p_k is maximal prime <= n and b_i = floor(n/p_i)- floor(n/p_i^2) + floor(n/p_i^3)-..., i.e., for exponents of primes of c-factorial we have an alternating sum, instead of the similar sum for exponents of primes for n! - Vladimir Shevelev, Oct 22 2014

PROG

(PARI) a(n) = prod(i=1, n, core(i)); \\ Michel Marcus, Aug 09 2013

CROSSREFS

Cf. A007913, A000142.

Sequence in context: A061558 A123144 A179215 * A056603 A019198 A155164

Adjacent sequences:  A069257 A069258 A069259 * A069261 A069262 A069263

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Apr 14 2002

STATUS

approved

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Last modified December 16 14:48 EST 2018. Contains 318167 sequences. (Running on oeis4.)