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A349619
Dirichlet convolution of A003415 with the Dirichlet inverse of A003557.
6
0, 1, 1, 3, 1, 3, 1, 7, 5, 5, 1, 7, 1, 7, 6, 15, 1, 9, 1, 13, 8, 11, 1, 15, 9, 13, 19, 19, 1, 14, 1, 31, 12, 17, 10, 17, 1, 19, 14, 29, 1, 20, 1, 31, 24, 23, 1, 31, 13, 25, 18, 37, 1, 27, 14, 43, 20, 29, 1, 30, 1, 31, 34, 63, 16, 32, 1, 49, 24, 34, 1, 33, 1, 37, 34, 55, 16, 38, 1, 61, 65, 41, 1, 44, 20, 43, 30, 71
OFFSET
1,4
LINKS
FORMULA
a(n) = Sum_{d|n} A003415(n/d) * A349340(d).
MATHEMATICA
f1[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f1 @@@ FactorInteger[n]; f[p_, e_] := -(p - 1)^(e - 1); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, s[#]*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]));
A349340(n) = { my(f=factor(n)); prod(i=1, #f~, -((f[i, 1]-1)^(f[i, 2]-1))); };
A349619(n) = sumdiv(n, d, A003415(n/d)*A349340(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 25 2021
STATUS
approved