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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.
2
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
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
KEYWORD
sign
AUTHOR
Antti Karttunen, Dec 16 2024
STATUS
approved