A318455 The 2-adic valuation of A318454(n).

0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 1, 0, 8, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 1, 0, 10, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 1, 0, 8, 0, 1, 0, 3, 0, 1, 0, 4, 0

Offset: 1

Author

Antti Karttunen and Andrew Howroyd, Aug 29 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001227, A007814, A318453, A318454.

Cf. also A046645, A317946, A318315, A318451.

Programs

Mathematica

f[1] = 1; f[n_] := f[n] = 1/2 (Sum[Mod[d, 2], {d, Divisors[n]}] - Sum[f[d] f[n/d], {d, Divisors[n][[2 ;; -2]]}]);
a[n_] := IntegerExponent[Denominator[f[n]], 2];
Array[a, 105] (* Jean-François Alcover, Sep 13 2018 *)

PARI

A318455(n) = valuation(A318454(n),2); \\ Needs also program from A318454.

Formula

a(n) = A007814(A318454(n)).