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A349620
Dirichlet convolution of A003415 with the Dirichlet inverse of A003958.
5
0, 1, 1, 3, 1, 2, 1, 8, 4, 2, 1, 5, 1, 2, 2, 20, 1, 7, 1, 5, 2, 2, 1, 12, 6, 2, 15, 5, 1, 3, 1, 48, 2, 2, 2, 17, 1, 2, 2, 12, 1, 3, 1, 5, 7, 2, 1, 28, 8, 11, 2, 5, 1, 24, 2, 12, 2, 2, 1, 7, 1, 2, 7, 112, 2, 3, 1, 5, 2, 3, 1, 40, 1, 2, 11, 5, 2, 3, 1, 28, 54, 2, 1, 7, 2, 2, 2, 12, 1, 10, 2, 5, 2, 2, 2, 64, 1, 15
OFFSET
1,4
LINKS
FORMULA
a(n) = Sum_{d|n} A003415(n/d) * A097945(d).
MATHEMATICA
f[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, MoebiusMu[#] * EulerPhi[#] * 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]));
A097945(n) = (moebius(n)*eulerphi(n)); \\ Also Dirichlet inverse of A003958.
A349620(n) = sumdiv(n, d, A003415(n/d)*A097945(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 25 2021
STATUS
approved