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

1,45

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A027750, A130799, A260073, A261476.

Sequence in context: A294927 A080224 A341508 * A341353 A010105 A341618

Adjacent sequences: A261485 A261486 A261487 * A261489 A261490 A261491

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 20 2015

Status

approved