A317844 Difference between A294898 and its Möbius transform (A297114).

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 3, 2, 0, 0, 1, 0, 0, 3, 7, 0, -6, 2, 9, 3, 1, 0, -2, 0, 0, 7, 14, 5, -9, 0, 15, 9, -4, 0, 3, 0, 5, 5, 18, 0, -14, 3, 14, 14, 7, 0, 2, 9, -3, 15, 24, 0, -24, 0, 25, 10, 0, 11, 12, 0, 12, 18, 15, 0, -29, 0, 33, 16, 13, 10, 14, 0, -12, 10, 37, 0, -23, 16, 38, 24, 1, 0, -16, 12, 16, 25

Offset: 1

Author

Antti Karttunen, Aug 09 2018

Keywords

• sign

Links

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

Crossrefs

Cf. A000203, A001065, A005187, A008683, A294898, A297114, A300244.

Programs

PARI

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A317844(n) = -sumdiv(n,d,(dA005187(d)-sigma(d)));

Formula

a(n) = -Sum_{d|n, dA008683(n/d)*A294898(d).

a(n) = A294898(n) - A297114(n).

a(n) = A300244(n) - A001065(n).