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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).
3
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
1,3
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).
PROG
(PARI) A325816(n) = { my(s=sigma(n)); sum(i=0, s, (1!=gcd(n-i, n-(s-i)))); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 29 2019
STATUS
approved