A379106 -id:A379106 - cp's OEIS frontend

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

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Antti Karttunen, Dec 16 2024

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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).

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

Cf. also A294898, A378755, A378757.

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(dA378990(d),0)); mapput(memoA378990,n,v); (v)));
A379107(n) = sumdiv(n,d,A033879(d)*A378990(n/d));

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

cp's OEIS Frontend

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.

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