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

1,5

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} A000120(d)*A323910(n/d).

Prog

(PARI)
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(d<n, A033879(n/d)*A323910(d), 0)); mapput(memoA323910, n, v); (v)));
A379106(n) = sumdiv(n, d, hammingweight(d)*A323910(n/d));

Crossrefs

Cf. A000120, A033879, A323910, A379107 (Dirichlet inverse).

Cf. also A294898, A378754, A378756.

Sequence in context: A125093 A294898 A297114 * A379107 A318448 A103516

Adjacent sequences: A379101 A379103 A379105 * A379107 A379108 A379109

Keyword

sign,new

Author

Antti Karttunen, Dec 16 2024

Status

approved