A069260 a(n) = core(1)*core(2)*...*core(n) where core(n) is the squarefree part of n (A007913).

1, 2, 6, 6, 30, 180, 1260, 2520, 2520, 25200, 277200, 831600, 10810800, 151351200, 2270268000, 2270268000, 38594556000, 77189112000, 1466593128000, 7332965640000, 153992278440000, 3387830125680000, 77920092890640000, 467520557343840000, 467520557343840000

Offset

1,2

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..538

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

Mathematica

core[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]); FoldList[Times, 1, core /@ Range[2, 23]] (* Amiram Eldar, Sep 05 2020 *)

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

Extensions

More terms from Amiram Eldar, Sep 05 2020

Status

approved