A318656 The 2-adic valuation of ratio A318649(n)/A318512(n); a(n) = 2*A007814(n) - A046645(n).

0, 1, -1, 1, -1, 0, -1, 2, -3, 0, -1, 0, -1, 0, -2, 1, -1, -2, -1, 0, -2, 0, -1, 1, -3, 0, -4, 0, -1, -1, -1, 2, -2, 0, -2, -2, -1, 0, -2, 1, -1, -1, -1, 0, -4, 0, -1, 0, -3, -2, -2, 0, -1, -3, -2, 1, -2, 0, -1, -1, -1, 0, -4, 2, -2, -1, -1, 0, -2, -1, -1, -1, -1, 0, -4, 0, -2, -1, -1, 0, -7, 0, -1, -1, -2, 0, -2, 1, -1, -3, -2, 0

Offset: 1

Author

Antti Karttunen, Sep 02 2018

Keywords

• sign

Comments

Also the 2-adic valuation of ratio A318681(n)/A299150(n) [which is equal to A318649(n)/A318512(n), but not represented in lowest terms], as well as the 2-adic valuation of A318680(n)/A299150(n) = A318511(n)/A318512(n).

Links

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

Crossrefs

Cf. A007814, A046645, A299150, A318440, A318511, A318512, A318513, A318649, A318655, A318680, A318681.

Cf. A318654 (positions of positive terms).

Programs

PARI

A007814(n) = valuation(n,2);
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A046644(n) = factorback(apply(e -> 2^A005187(e),factor(n)[,2]));
A318656(n) = ((2*A007814(n))-A007814(A046644(n)));

Formula

a(n) = A318655(n) - A318513(n).

a(n) = A007814(n) - A318440(n).

a(n) = 2*A007814(n) - A046645(n) = A007814(n^2) - A046645(n).