A305809 Dirichlet convolution of A003415 (Arithmetic derivative) with itself.

0, 0, 0, 1, 0, 2, 0, 8, 1, 2, 0, 18, 0, 2, 2, 40, 0, 22, 0, 22, 2, 2, 0, 96, 1, 2, 12, 26, 0, 40, 0, 160, 2, 2, 2, 147, 0, 2, 2, 128, 0, 48, 0, 34, 28, 2, 0, 400, 1, 34, 2, 38, 0, 156, 2, 160, 2, 2, 0, 276, 0, 2, 32, 560, 2, 64, 0, 46, 2, 56, 0, 680, 0, 2, 36, 50, 2, 72, 0, 560, 90, 2, 0, 348, 2, 2, 2, 224, 0, 346, 2, 58, 2, 2, 2, 1440, 0, 46, 40, 267, 0, 88

Offset: 1

Author

Antti Karttunen, Jun 13 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A300251, A300252.

Cf. A008578 (positions of 0's), A001248 (of 1's), A006881 (of 2's).

Programs

PARI

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A305809(n) = sumdiv(n,d,A003415(n/d)*A003415(d));

Formula

a(n) = Sum_{d|n} A003415(n/d)*A003415(d).