A318505 Sum of divisors of n, up to, but not including the second largest of them A032742(n); a(1) = 0 by convention.

0, 0, 0, 1, 0, 3, 0, 3, 1, 3, 0, 10, 0, 3, 4, 7, 0, 12, 0, 12, 4, 3, 0, 24, 1, 3, 4, 14, 0, 27, 0, 15, 4, 3, 6, 37, 0, 3, 4, 30, 0, 33, 0, 18, 18, 3, 0, 52, 1, 18, 4, 20, 0, 39, 6, 36, 4, 3, 0, 78, 0, 3, 20, 31, 6, 45, 0, 24, 4, 39, 0, 87, 0, 3, 24, 26, 8, 51, 0, 66, 13, 3, 0, 98, 6, 3, 4, 48, 0, 99, 8, 30, 4, 3, 6, 108, 0, 24, 24, 67, 0, 63, 0, 54, 52

Offset: 1

Author

Antti Karttunen, Aug 27 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A001065, A013661, A032742, A318504, A318506, A318507, A318508.

Programs

PARI

A001065(n) = (sigma(n)-n);
A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318505(n) = if(1==n,0,A001065(n)-A032742(n));
A318505(n) = sumdiv(n,d,(d<A032742(n))*d); \\ Alternatively.

Formula

a(1) = 0; for n > 1, a(n) = A001065(n) - A032742(n).

Sum_{k=1..n} a(k) ~ (zeta(2)/2 - 1/2 - c) * n^2, where c is defined in the corresponding formula in A032742. - Amiram Eldar, Dec 21 2024