A261488 Number of triples (x, y, x mod y) such that x > y are divisors of n and x mod y is an anti-divisor of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 3, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 3, 0, 1, 0, 0, 0, 0

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 20 2015

Keywords

• nonn

Comments

An anti-divisor of n is a number d in the range [2,n-1] which does not divide n and is either a (necessarily odd) divisor of 2n-1 or 2n+1, or a (necessarily even) divisor of 2n.

a(n) = 0 if n is a prime power.

Examples

			a(45) = 2 with triples (5, 3, 5 mod 3) and (15, 9, 15 mod 9) since 3, 5, 9, and 15 are divisors of 45 and 5 mod 3 = 2 and 15 mod 9 = 6 are anti-divisors of 45.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027750, A130799, A260073, A261476.

Programs

PARI

a(n)=my(d=divisors(n)); sum(i=1,#d-1, sum(j=i+1,#d, my(z=d[j]%d[i]); z && n%z && if(z%2, (2*n+1)%z==0 || (2*n-1)%z==0, (2*n)%z==0))) \\ Charles R Greathouse IV, Aug 26 2015