A329643 a(n) = Sum_{d|n} [-1 == A008683(n/d)] * A323244(d), where A323244(x) gives the deficiency of A156552(x).

0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 6, 0, 2, 2, 6, 0, 4, 0, 7, 2, 2, 0, 16, 1, 2, 0, 18, 0, 11, 0, 6, 2, 2, 2, 22, 0, 2, 2, 24, 0, 17, 0, 20, 2, 2, 0, 28, 1, 1, 2, 48, 0, 16, 2, 28, 2, 2, 0, 39, 0, 2, -3, 30, 2, 36, 0, 84, 2, 19, 0, 36, 0, 2, -2, 258, 2, 38, 0, 28, 4, 2, 0, 69, 2, 2, 2, 72, 0, 31, 2, 228, 2, 2, 2, 76, 0, 4, 14, 37, 0, 94, 0, 136, -3

Offset: 1

Author

Antti Karttunen, Nov 21 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A006881, A008683, A156552, A323243, A323244, A329642, A329644.

Cf. A329646 (inverse Möbius transform).

Programs

PARI

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A323243(n) = if(1==n,0,sigma(A156552(n)));
A329643(n) = sumdiv(n,d,(-1==moebius(n/d))*((2*A156552(d))-A323243(d)));

Formula

a(n) = Sum_{d|n} [-1 == A008683(n/d)] * (2*A156552(d) - A323243(d)).

a(n) = A329642(n) - A329644(n).

For all n, a(A000040(n)) = 0, a(A006881(n)) = 2.