A318442 a(n) = Sum_{d|n} [moebius(n/d) < 0]*A033879(d).

0, 1, 1, 1, 1, 3, 1, 1, 2, 5, 1, 1, 1, 7, 6, 1, 1, 5, 1, 3, 8, 11, 1, -3, 4, 13, 5, 5, 1, 9, 1, 1, 12, 17, 10, -7, 1, 19, 14, -1, 1, 15, 1, 9, 11, 23, 1, -11, 6, 21, 18, 11, 1, 11, 14, 1, 20, 29, 1, -17, 1, 31, 15, 1, 16, 27, 1, 15, 24, 29, 1, -31, 1, 37, 25, 17, 16, 33, 1, -9, 14, 41, 1, -15, 20, 43, 30, 5, 1, -1, 18, 21, 32, 47, 22, -27, 1

Offset: 1

Author

Antti Karttunen, Aug 26 2018

Keywords

• sign

Links

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

Crossrefs

Cf. A033879, A083254, A318320, A318325, A318441.

Programs

PARI

A318442(n) = sumdiv(n,d,(-1==moebius(n/d))*(d+d-sigma(d)));

Formula

a(n) = Sum_{d|n} [A008683(n/d) == 1]*A033879(d).

a(n) = A318320(n) - A318326(n).

A083254(n) = A318441(n) - a(n).