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

1,6

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)

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.

Prog

(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)));

Crossrefs

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

Cf. A329646 (inverse Möbius transform).

Sequence in context: A071459 A319164 A070288 * A352697 A165414 A330868

Adjacent sequences: A329640 A329641 A329642 * A329644 A329645 A329646

Keyword

sign

Author

Antti Karttunen, Nov 21 2019

Status

approved