A319683 - OEIS

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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

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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));