A319683 Sum of A003415(d) over the proper divisors d of n, where A003415 is arithmetic derivative.

0, 0, 0, 1, 0, 2, 0, 5, 1, 2, 0, 11, 0, 2, 2, 17, 0, 13, 0, 13, 2, 2, 0, 39, 1, 2, 7, 15, 0, 23, 0, 49, 2, 2, 2, 54, 0, 2, 2, 49, 0, 27, 0, 19, 16, 2, 0, 115, 1, 19, 2, 21, 0, 61, 2, 59, 2, 2, 0, 98, 0, 2, 18, 129, 2, 35, 0, 25, 2, 31, 0, 170, 0, 2, 20, 27, 2, 39, 0, 149, 34, 2, 0, 120, 2, 2, 2, 79, 0, 120, 2, 31, 2, 2, 2, 307, 0, 25, 22, 92, 0

Offset: 1

Author

Antti Karttunen, Oct 02 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A319684.

Cf. also A300251, A300252, A305809, A317835.

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
A319683(n) = sumdiv(n,d,(dA003415(d));

Formula

a(n) = Sum_{d|n, dA003415(d).

a(n) = A319684(n) - A003415(n).