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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 14 2002
EXTENSIONS
More terms from Amiram Eldar, Sep 05 2020
STATUS
approved