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A323882
Sum of A126760 and its Dirichlet inverse.
9
2, 0, 0, 1, 0, 2, 0, 1, 1, 4, 0, 1, 0, 6, 4, 1, 0, 1, 0, 2, 6, 8, 0, 1, 4, 10, 1, 3, 0, 0, 0, 1, 8, 12, 12, 1, 0, 14, 10, 2, 0, 0, 0, 4, 2, 16, 0, 1, 9, 14, 12, 5, 0, 1, 16, 3, 14, 20, 0, 2, 0, 22, 3, 1, 20, 0, 0, 6, 16, 12, 0, 1, 0, 26, 14, 7, 24, 0, 0, 2, 1, 28, 0, 3, 24, 30, 20, 4, 0, 2, 30, 8, 22, 32, 28, 1, 0, 25, 4, 9, 0, 0, 0, 5, 12
OFFSET
1,1
COMMENTS
From Antti Karttunen, Aug 18 2021: (Start)
No negative terms in range 1 .. 2^20.
Apparently zeros occur only on (some of the) positions given by A030059, with exceptions for example on n = 70, 105, 110, 130, 154, etc, where a(n) > 0.
(End)
FORMULA
a(n) = A126760(n) + A323881(n).
For n > 1, a(n) = -Sum_{d|n, 1<d<n} A126760(d) * A323881(n/d). - Antti Karttunen, Aug 18 2021
PROG
(PARI)
up_to = 20000;
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v
v323881 = DirInverseCorrect(vector(up_to, n, A126760(n)));
A323881(n) = v323881[n];
A323882(n) = (A126760(n)+A323881(n));
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Feb 08 2019
STATUS
approved