A376556 - OEIS

%I #7 Sep 28 2024 07:37:35

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,2,4,6,2,2,0,0,1,

%T 2,0,0,0,2,0,0,0,1,0,1,6,8,0,0,0,4,4,6,2,2,0,1,1,1,1,1,1,2,0,0,0,0,0,

%U 0,0,2,0,0,0,1,0,2,4,4,0,0,4,8,2,3,6,8

%N The number of non-unitary square divisors of binomial(n, floor(n/2)).

%H Amiram Eldar, <a href="/A376556/b376556.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A056626(A001405(n)).

%t f1[p_, e_] := 1 + Floor[e/2]; f2[p_, e_] := 2^(1 - Mod[e, 2]); a[0] = a[1] = 0; a[n_] := Times @@ f1 @@@ (fct = FactorInteger[Binomial[n, Floor[n/2]]]) - Times @@ f2 @@@ fct; Array[a, 60, 0]

%o (PARI) a(n) = {my(e = factor(binomial(n, n\2))[, 2]); vecprod(apply(x -> x\2 + 1, e)) - vecprod(apply(x -> 1 << (1 - x%2), e));}

%Y Cf. A001405, A056061, A056626, A376553, A376554, A376555.

%K nonn

%O 0,27

%A _Amiram Eldar_, Sep 28 2024