A360121 Dirichlet convolution of A342001 with A342002.

0, 1, 1, 3, 1, 11, 1, 7, 7, 15, 1, 26, 1, 17, 20, 19, 1, 66, 1, 48, 22, 55, 1, 56, 9, 25, 44, 52, 1, 160, 1, 47, 60, 67, 26, 133, 1, 33, 30, 112, 1, 186, 1, 140, 135, 79, 1, 128, 9, 86, 72, 80, 1, 256, 64, 130, 38, 91, 1, 372, 1, 43, 155, 85, 34, 406, 1, 168, 84, 262, 1, 241, 1, 99, 127, 156, 66, 472, 1, 336, 130

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) * A342002(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]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A342001(n) = (A003415(n) / A003557(n));
A342002(n) = A342001(A276086(n));
A360121(n) = sumdiv(n, d, A342001(n/d)*A342002(d));

Crossrefs

Cf. A003415, A342001, A342002, A360122 (parity of terms).

Cf. also A347389, A359425.

Sequence in context: A119632 A201131 A277790 * A339175 A134761 A166752

Adjacent sequences: A360118 A360119 A360120 * A360122 A360123 A360124

Keyword

nonn

Author

Antti Karttunen, Feb 19 2023

Status

approved