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A349621
Dirichlet convolution of A003415 with the Dirichlet inverse of A003959.
5
0, 1, 1, 1, 1, -2, 1, 0, 2, -2, 1, -3, 1, -2, -2, -4, 1, -5, 1, -3, -2, -2, 1, -4, 4, -2, 3, -3, 1, 3, 1, -16, -2, -2, -2, -7, 1, -2, -2, -4, 1, 3, 1, -3, -5, -2, 1, -4, 6, -9, -2, -3, 1, -12, -2, -4, -2, -2, 1, 5, 1, -2, -5, -48, -2, 3, 1, -3, -2, 3, 1, -8, 1, -2, -9, -3, -2, 3, 1, -4, 0, -2, 1, 5, -2, -2, -2, -4
OFFSET
1,6
LINKS
FORMULA
a(n) = Sum_{d|n} A003415(n/d) * A063441(d).
MATHEMATICA
f[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, MoebiusMu[#] * DivisorSigma[1, #] * d[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 25 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A063441(n) = (moebius(n)*sigma(n)); \\ Also Dirichlet inverse of A003959.
A349621(n) = sumdiv(n, d, A003415(n/d)*A063441(d));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 25 2021
STATUS
approved