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Even bisection of A318256.
1

%I #14 Mar 08 2019 03:27:44

%S 1,2,6,6,10,6,210,2,30,210,110,30,546,14,30,462,1190,6,51870,70,2310,

%T 2310,322,210,6630,286,330,798,290,30,930930,1430,1122,82110,70,330,

%U 21111090,38038,390,210,536690,39270,7489482,10010,62790,4470510,687610,462

%N Even bisection of A318256.

%C The ratio sequence of a(n)/A006955(n) begins: 1,1,1,1,1,1,1,1,1,5,1,5,1,7,1,1,7,1,1,35, ...

%C This divisibility by A006955 was confirmed by _Peter Luschny_ in the SeqFan mailing list.

%H Jean-François Alcover, <a href="/A306745/b306745.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (denominator of B(2n,x)) / (the squarefree kernel of 2n+1), where B(2n,x) is the 2n-th Bernoulli polynomial.

%t sfk[n_] := Times @@ FactorInteger[n][[All, 1]];

%t a[n_] := (BernoulliB[2 n, x] // Together // Denominator)/sfk[2 n + 1];

%t Table[a[n], {n, 0, 60}]

%Y Cf. A006955, A318256.

%K nonn

%O 0,2

%A _Jean-François Alcover_ and _Paul Curtz_, Mar 07 2019