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

1,4

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A001227, A007814, A318453, A318454.

Cf. also A046645, A317946, A318315, A318451.

Sequence in context: A123878 A284148 A108197 * A363029 A049769 A117179

Adjacent sequences: A318452 A318453 A318454 * A318456 A318457 A318458

Keyword

nonn

Author

Antti Karttunen and Andrew Howroyd, Aug 29 2018

Status

approved