cp's OEIS Frontend

A272608 Number of positive integers k such that both n/(k + 2^x) and n/(n/k - 2^y) are integers for some nonnegative x, y.

%I A272608 #15 Nov 11 2016 10:42:17
%S A272608 0,1,1,2,1,2,0,3,1,2,0,4,0,0,1,4,1,2,0,3,1,0,0,6,0,0,0,0,0,3,0,5,2,2,
%T A272608 1,4,0,0,0,4,0,2,0,0,1,0,0,8,0,0,0,0,0,0,0,1,1,0,0,5,0,0,1,6,2,4,0,2,
%U A272608 0,1,0,6,0,0,0,0,1,0,0,5,0,0,0,3,0,0,0,0,0,2
%N A272608 Number of positive integers k such that both n/(k + 2^x) and n/(n/k - 2^y) are integers for some nonnegative x, y.
%C A272608 Where k, k + 2^x, n/k, n/k - 2^y, n/(k + 2^x) and n/(n/k - 2^y) are divisors of n.
%F A272608 a(2^n) = n, a(A092506(n)) = 1.
%e A272608 a(9) = 1 because both 9/(1 + 2^1) = 3 and 9/(9/1 - 2^4) = 1 are integers.
%e A272608 a(68) = 3 because (1) 68/(1 + 2^0) = 34 and 68/(68 - 2^6) = 17, (2) 68/(2 + 2^1) = 17 and 68/(34 - 2^5) = 34, and (3) 68/(4 + 2^6) = 1 and 68/(17 - 2^4) = 68 are all integers.
%o A272608 (PARI) t1(n,k)=for(x=0,logint(n,2), if(n%(k+2^x)==0, return(1))); 0
%o A272608 t2(n,d)=for(y=0,logint(d-1,2), if(n%(d-2^y)==0, return(1))); 0
%o A272608 a(n)=sumdiv(n,k, k<n && t1(n,k) && t2(n,n/k)) \\ _Charles R Greathouse IV_, Nov 09 2016
%Y A272608 Cf. A027750, A092506, A277994.
%K A272608 nonn
%O A272608 1,4
%A A272608 _Juri-Stepan Gerasimov_, Nov 09 2016
%E A272608 a(68), a(70), a(90) corrected by _Charles R Greathouse IV_, Nov 09 2016