A069260 - OEIS

%I #24 Sep 05 2020 07:45:23

%S 1,2,6,6,30,180,1260,2520,2520,25200,277200,831600,10810800,151351200,

%T 2270268000,2270268000,38594556000,77189112000,1466593128000,

%U 7332965640000,153992278440000,3387830125680000,77920092890640000,467520557343840000,467520557343840000

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

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

%H Amiram Eldar, <a href="/A069260/b069260.txt">Table of n, a(n) for n = 1..538</a>

%F 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

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

%o (PARI) a(n) = prod(i=1, n, core(i)); \\ _Michel Marcus_, Aug 09 2013

%Y Cf. A007913, A000142.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Apr 14 2002

%E More terms from _Amiram Eldar_, Sep 05 2020