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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..538
Programs
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Mathematica
core[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]); FoldList[Times, 1, core /@ Range[2, 23]] (* Amiram Eldar, Sep 05 2020 *)
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PARI
a(n) = prod(i=1, n, core(i)); \\ Michel Marcus, Aug 09 2013
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
Extensions
More terms from Amiram Eldar, Sep 05 2020
Comments