A325816 Number of ways to form the sum sigma(n) = x+y, so that n-x and n-y are not coprime, with x and y in range 0..sigma(n).

0, 0, 2, 0, 3, 11, 5, 0, 2, 10, 7, 15, 9, 13, 17, 0, 9, 14, 13, 22, 19, 19, 13, 41, 2, 27, 23, 55, 17, 49, 23, 0, 33, 31, 27, 4, 25, 31, 31, 55, 25, 65, 31, 43, 53, 45, 25, 71, 2, 14, 53, 67, 29, 81, 37, 61, 43, 49, 31, 113, 45, 55, 57, 0, 43, 97, 47, 77, 69, 73, 47, 74, 49, 61, 67, 95, 49, 113, 55, 101, 2, 67, 43, 129, 55, 81, 81, 91, 49

Offset: 1

Author

Antti Karttunen, May 29 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A324213, A325815.

Programs

PARI

A325816(n) = { my(s=sigma(n)); sum(i=0, s, (1!=gcd(n-i, n-(s-i)))); };

Formula

a(n) = Sum_{i=0..sigma(n)} [1 <> gcd(n-i,n-(sigma(n)-i))], where [ ] is the Iverson bracket and sigma(n) is A000203(n).

a(n) = 1 + A000203(n) - A324213(n).