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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jun 11 2018

Keywords

• nonn

Comments

a(n) is the number of terms of A000051 less than n that divide n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000051, A209229, A305436.

Cf. also A305426.

Programs

Mathematica

Table[DivisorSum[n, 1 &, And[IntegerQ@ Log2[# - 1], # < n] &], {n, 105}] (* Michael De Vlieger, Jun 11 2018 *)

PARI

A209229(n) = (n && !bitand(n,n-1));
A305435(n) = sumdiv(n,d,(dA209229(d-1));

Formula

a(n) = Sum_{d|n, dA209229(d-1).

a(n) = A305436(n) - A209229(n-1).