cp's OEIS Frontend

A305426 Number of proper divisors of n of the form 2^k - 1 for k >= 1.

%I A305426 #7 Jun 12 2018 10:17:32
%S A305426 0,1,1,1,1,2,1,1,2,1,1,2,1,2,2,1,1,2,1,1,3,1,1,2,1,1,2,2,1,3,1,1,2,1,
%T A305426 2,2,1,1,2,1,1,3,1,1,3,1,1,2,2,1,2,1,1,2,1,2,2,1,1,3,1,2,3,1,1,2,1,1,
%U A305426 2,2,1,2,1,1,3,1,2,2,1,1,2,1,1,3,1,1,2,1,1,3,2,1,3,1,1,2,1,2,2,1,1,2,1,1,4
%N A305426 Number of proper divisors of n of the form 2^k - 1 for k >= 1.
%C A305426 a(n) is the number of terms of A000225 less than n that divide n.
%H A305426 Antti Karttunen, <a href="/A305426/b305426.txt">Table of n, a(n) for n = 1..65537</a>
%F A305426 a(n) = Sum_{d|n, d<n} A036987(d).
%F A305426 a(n) = A154402(n) - A036987(n).
%t A305426 Table[DivisorSum[n, 1 &, And[IntegerQ@ Log2[# + 1], # < n] &], {n, 105}] (* _Michael De Vlieger_, Jun 11 2018 *)
%o A305426 (PARI)
%o A305426 A209229(n) = (n && !bitand(n,n-1));
%o A305426 A036987(n) = A209229(1+n);
%o A305426 A305426(n) = sumdiv(n,d,(d<n)*A036987(d));
%Y A305426 Cf. A000225, A036987, A154402.
%Y A305426 Cf. also A305435.
%K A305426 nonn
%O A305426 1,6
%A A305426 _Antti Karttunen_, Jun 11 2018