A347959 Dirichlet convolution of A342001 with A345000.

0, 1, 1, 3, 1, 7, 1, 7, 3, 9, 1, 18, 1, 11, 10, 15, 1, 16, 1, 24, 12, 15, 1, 40, 3, 17, 6, 30, 1, 54, 1, 39, 16, 21, 14, 41, 1, 23, 18, 54, 1, 72, 1, 42, 25, 27, 1, 92, 3, 24, 22, 52, 1, 30, 18, 68, 24, 33, 1, 132, 1, 35, 35, 73, 20, 96, 1, 60, 28, 92, 1, 99, 1, 41, 27, 66, 20, 114, 1, 120, 10, 45, 1, 176, 24, 47

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..11550

Index entries for sequences related to primorial base

Formula

a(n) = Sum_{d|n} A342001(n/d) * A345000(d).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n), A003415(A276086(n)));
A347959(n) = sumdiv(n, d, A342001(n/d)*A345000(d));

Crossrefs

Cf. A003415, A327860, A342001, A345000.

Cf. also A347234, A347954, A347958.

Sequence in context: A347234 A324865 A316553 * A347963 A186428 A323599

Adjacent sequences: A347956 A347957 A347958 * A347960 A347961 A347962

Keyword

nonn,base

Author

Antti Karttunen, Sep 21 2021

Status

approved