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

1,6

Links

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

Formula

a(n) = Sum_{d|n, d<n} A003415(d).

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

Prog

(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, (d<n)*A003415(d));

Crossrefs

Cf. A003415, A319684.

Cf. also A300251, A300252, A305809, A317835.

Sequence in context: A188445 A350158 A327806 * A294137 A246723 A339168

Adjacent sequences: A319680 A319681 A319682 * A319684 A319685 A319686

Keyword

nonn

Author

Antti Karttunen, Oct 02 2018

Status

approved