cp's OEIS Frontend

A305436 Number of divisors of n of the form 2^k + 1 for k >= 0.

%I A305436 #13 Dec 31 2023 03:40:41
%S A305436 0,1,1,1,1,2,0,1,2,2,0,2,0,1,2,1,1,3,0,2,1,1,0,2,1,1,2,1,0,3,0,1,2,2,
%T A305436 1,3,0,1,1,2,0,2,0,1,3,1,0,2,0,2,2,1,0,3,1,1,1,1,0,3,0,1,2,1,2,3,0,2,
%U A305436 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 A305436 Number of divisors of n of the form 2^k + 1 for k >= 0.
%C A305436 a(n) is the number of terms of A000051 that divide n.
%H A305436 Antti Karttunen, <a href="/A305436/b305436.txt">Table of n, a(n) for n = 1..65537</a>
%F A305436 a(n) = Sum_{d|n} A209229(d-1).
%F A305436 a(n) = A305435(n) + A209229(n-1).
%F A305436 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A323482 = 1.264499... . - _Amiram Eldar_, Dec 31 2023
%t A305436 Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# - 1] &], {n, 105}] (* _Michael De Vlieger_, Jun 11 2018 *)
%o A305436 (PARI)
%o A305436 A209229(n) = (n && !bitand(n,n-1));
%o A305436 A305436(n) = sumdiv(n,d,A209229(d-1));
%Y A305436 Cf. A000051, A209229, A292315 (positions of zeros), A305435, A323482.
%Y A305436 Cf. also A154402.
%K A305436 nonn
%O A305436 1,6
%A A305436 _Antti Karttunen_, Jun 11 2018