cp's OEIS Frontend

A305435 Number of proper divisors of n of the form 2^k + 1 for k >= 0.

%I A305435 #9 Jun 12 2018 10:17:25
%S A305435 0,0,0,1,0,2,0,1,1,2,0,2,0,1,2,1,0,3,0,2,1,1,0,2,1,1,2,1,0,3,0,1,1,2,
%T A305435 1,3,0,1,1,2,0,2,0,1,3,1,0,2,0,2,2,1,0,3,1,1,1,1,0,3,0,1,2,1,1,3,0,2,
%U A305435 1,2,0,3,0,1,2,1,0,2,0,2,2,1,0,2,2,1,1,1,0,4,0,1,1,1,1,2,0,1,3,2,0,3,0,1,2
%N A305435 Number of proper divisors of n of the form 2^k + 1 for k >= 0.
%C A305435 a(n) is the number of terms of A000051 less than n that divide n.
%H A305435 Antti Karttunen, <a href="/A305435/b305435.txt">Table of n, a(n) for n = 1..65537</a>
%F A305435 a(n) = Sum_{d|n, d<n} A209229(d-1).
%F A305435 a(n) = A305436(n) - A209229(n-1).
%t A305435 Table[DivisorSum[n, 1 &, And[IntegerQ@ Log2[# - 1], # < n] &], {n, 105}] (* _Michael De Vlieger_, Jun 11 2018 *)
%o A305435 (PARI)
%o A305435 A209229(n) = (n && !bitand(n,n-1));
%o A305435 A305435(n) = sumdiv(n,d,(d<n)*A209229(d-1));
%Y A305435 Cf. A000051, A209229, A305436.
%Y A305435 Cf. also A305426.
%K A305435 nonn
%O A305435 1,6
%A A305435 _Antti Karttunen_, Jun 11 2018