A318448 a(n) = Sum_{d|n} A294898(d), where A294898(d) = A005187(d) - sigma(d).

0, 0, 0, 0, 2, -2, 3, 0, 3, 2, 7, -8, 9, 4, 4, 0, 14, -4, 15, -2, 10, 12, 18, -22, 18, 16, 13, 1, 24, -14, 25, 0, 23, 26, 24, -31, 33, 28, 27, -14, 37, -6, 38, 13, 15, 34, 41, -52, 41, 22, 40, 19, 48, -10, 42, -10, 45, 46, 53, -76, 55, 48, 29, 0, 55, 12, 63, 34, 57, 18, 66, -98, 69, 64, 42, 37, 64, 16, 73, -42, 51, 72, 78, -74, 74, 74, 73, 6

Offset: 1

Author

Antti Karttunen, Aug 27 2018

Keywords

• sign

Comments

Inverse Möbius transform of A294898.

Links

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

Crossrefs

Cf. A000203, A005187, A007429, A093653, A294898, A296075, A318446, A318447.

Cf. also A297114, A317844.

Programs

PARI

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A294898(n) = (A005187(n) - sigma(n));
A318448(n) = sumdiv(n,d,A294898(d));

Formula

a(n) = Sum_{d|n} A294898(d).

a(n) = A318447(n) + A294898(n).

a(n) = A318446(n) - A007429(n).

a(n) = A296075(n) - A093653(n).