A294904 Number of divisors of n that are in A175526.

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 3, 0, 3, 0, 3, 1, 1, 0, 5, 0, 1, 2, 3, 0, 4, 0, 4, 1, 1, 1, 6, 0, 1, 1, 5, 0, 4, 0, 3, 3, 1, 0, 7, 1, 2, 1, 3, 0, 5, 1, 5, 1, 1, 0, 8, 0, 1, 3, 5, 1, 4, 0, 3, 1, 4, 0, 9, 0, 1, 2, 3, 1, 4, 0, 7, 3, 1, 0, 8, 1, 1, 1, 5, 0, 8, 1, 3, 1, 1, 0, 9, 0, 3, 3, 5, 0, 4, 0, 5, 4, 1, 0, 9, 0, 4, 0, 7, 0, 4, 1, 3, 3, 1, 0, 12

Offset: 1

Author

Antti Karttunen, Nov 10 2017

Keywords

• nonn
• base

Comments

Number of terms of A175526 that divide n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000

Crossrefs

Cf. A000120, A175526, A292257, A294901, A294902, A294903, A294905.

Cf. also A294894.

Programs

Mathematica

q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] > 2 * DigitCount[n, 2, 1]; a[n_] := DivisorSum[n, 1 &, q[#] &]; Array[a, 100] (* Amiram Eldar, Jul 20 2023 *)

PARI

A292257(n) = sumdiv(n,d,(dA294905(n) = (A292257(n) <= hammingweight(n));
A294904(n) = sumdiv(n,d,(0==A294905(d)));

Formula

a(n) = Sum_{d|n} (1-A294905(d)).

a(n) = 1 + (A294902(n)-A294905(n)).

a(n) + A294903(n) = A000005(n).