A379107 Dirichlet convolution of A033879 and A378990, where A033879 is the deficiency of n, and A378990 is the Dirichlet inverse of the binary weight of n.

1, 0, 0, 0, 2, -2, 3, 0, 3, -2, 7, -4, 9, -2, -2, 0, 14, -4, 15, -4, 1, -2, 18, -8, 12, -2, 4, -4, 24, -10, 25, 0, 2, -2, 7, -8, 33, -2, 0, -8, 37, -12, 38, -4, 2, -2, 41, -16, 29, -8, -2, -4, 48, -14, 13, -8, 0, -2, 53, -20, 55, -2, -1, 0, 20, -20, 63, -4, 3, -16, 66, -16, 69, -2, -6, -4, 24, -24, 73, -16, 24, -2, 78

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to sigma(n).

Formula

a(n) = Sum_{d|n} A033879(d)*A378990(n/d).

Prog

(PARI)
A033879(n) = (n+n-sigma(n));
memoA378990 = Map();
A378990(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378990, n, &v), v, v = -sumdiv(n, d, if(d<n, hammingweight(n/d)*A378990(d), 0)); mapput(memoA378990, n, v); (v)));
A379107(n) = sumdiv(n, d, A033879(d)*A378990(n/d));

Crossrefs

Cf. A000120, A033879, A378990, A379106 (Dirichlet inverse).

Cf. also A294898, A378755, A378757.

Sequence in context: A294898 A297114 A379106 * A318448 A103516 A233558

Adjacent sequences: A379104 A379105 A379106 * A379108 A379109 A379110

Keyword

sign

Author

Antti Karttunen, Dec 16 2024

Status

approved