A329642 a(n) = Sum_{d|n} [1 == A008683(n/d)] * A323244(d), where A323244(x) gives the deficiency of A156552(x).

0, 1, 1, 2, 1, 4, 1, 6, 0, 5, 1, 11, 1, 16, 2, 6, 1, 13, 1, 19, -3, 18, 1, 24, -4, 46, 4, 23, 1, 13, 1, 30, 14, 82, -2, 18, 1, 256, -12, 24, 1, 39, 1, 67, 9, 226, 1, 52, -12, 20, 8, 131, 1, 28, -19, 72, -12, 748, 1, 53, 1, 1362, 17, 22, 10, 45, 1, 215, 254, 43, 1, 48, 1, 3838, 11, 407, -10, 109, 1, 84, -12, 5458, 1, 48, -72, 12250, -348, 32, 1, 18

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. A008683, A156552, A323243, A323244, A329643, A329644.

Cf. A329645 (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)));
A329642(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) = A329643(n) + A329644(n).