A305439 a(n) = A046645(n) - A007949(n); the 2-adic valuation of A317932.

0, 1, 0, 3, 1, 1, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 4, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 1, 8, 1, 2, 2, 4, 1, 2, 1, 5, 1, 2, 1, 4, 2, 2, 1, 7, 3, 4, 1, 4, 1, 2, 2, 5, 1, 2, 1, 4, 1, 2, 2, 10, 2, 2, 1, 4, 1, 3, 1, 5, 1, 2, 3, 4, 2, 2, 1, 8, 3, 2, 1, 4, 2, 2, 1, 5, 1, 3, 2, 4, 1, 2, 2, 8, 1, 4, 2, 6, 1, 2, 1, 5, 2

Offset: 1

Author

Antti Karttunen, Sep 02 2018

Keywords

• nonn

Comments

Apart from a(1) and a(3), all other terms are positive.

Links

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

Crossrefs

Cf. A007814, A007949, A046645, A317932.

Cf. also A318440.

Programs

PARI

A007949(n) = valuation(n,3);
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A046645(n) = vecsum(apply(e -> A005187(e),factor(n)[,2]));
A305439(n) = A046645(n) - A007949(n);

Formula

a(n) = A046645(n) - A007949(n).

a(n) = A007814(A317932(n)).