A379107 -id:A379107 - cp's OEIS frontend

A379106 Dirichlet convolution of A000120 and A323910, where A323910 is the Dirichlet inverse of the deficiency of n, and A000120 is 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, -8, 2, -4, 4, -24, 2, -25, 0, -2, 2, 5, 12, -33, 2, 0, 8, -37, 0, -38, 4, 10, 2, -41, 16, -20, 0, 2, 4, -48, 2, 15, 8, 0, 2, -53, 12, -55, 2, 19, 0, 16, -8, -63, 4, -3, -4, -66, 32, -69, 2, -2, 4, 18, -12, -73, 16, -15, 2, -78, 8, 30

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, A323910, A379107 (Dirichlet inverse).

Cf. also A294898, A378754, A378756.

A033879(n) = (n+n-sigma(n));
memoA323910 = Map();
A323910(n) = if(1==n,1,my(v); if(mapisdefined(memoA323910,n,&v), v, v = -sumdiv(n,d,if(dA033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));
A379106(n) = sumdiv(n,d,hammingweight(d)*A323910(n/d));

a(n) = Sum_{d|n} A000120(d)*A323910(n/d).

cp's OEIS Frontend

A379106 Dirichlet convolution of A000120 and A323910, where A323910 is the Dirichlet inverse of the deficiency of n, and A000120 is the binary weight of n.

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