cp's OEIS Frontend

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.

%I A261488 #21 Oct 05 2017 15:47:40
%S A261488 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,
%T A261488 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,
%U A261488 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
%N 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.
%C A261488 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.
%C A261488 a(n) = 0 if n is a prime power.
%H A261488 Antti Karttunen, <a href="/A261488/b261488.txt">Table of n, a(n) for n = 1..10000</a>
%e A261488 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.
%o A261488 (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
%Y A261488 Cf. A027750, A130799, A260073, A261476.
%K A261488 nonn
%O A261488 1,45
%A A261488 _Juri-Stepan Gerasimov_, Aug 20 2015