A294901 Number of proper divisors of n that are in A257691.

0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 3, 1, 3, 3, 3, 1, 3, 2, 3, 2, 3, 1, 4, 1, 2, 3, 3, 3, 3, 1, 3, 3, 3, 1, 4, 1, 3, 3, 3, 1, 3, 2, 4, 3, 3, 1, 3, 3, 3, 3, 3, 1, 4, 1, 3, 3, 2, 3, 4, 1, 3, 3, 4, 1, 3, 1, 3, 4, 3, 3, 4, 1, 3, 2, 3, 1, 4, 3, 3, 3, 3, 1, 4, 3, 3, 3, 3, 3, 3, 1, 3, 3, 4, 1, 4, 1, 3, 4, 3, 1, 3, 1, 4, 3, 3, 1, 4, 3, 3, 3, 3, 3, 4

Offset: 1

Author

Antti Karttunen, Nov 10 2017

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A000120, A032741, A257691, A292257, A294902, A294903, A294904, A294905.

Cf. also A294891.

Programs

Mathematica

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

PARI

A292257(n) = sumdiv(n,d,(dA294905(n) = (A292257(n) <= hammingweight(n));
A294901(n) = sumdiv(n,d,(dA294905(d));

Formula

a(n) = Sum_{d|n, dA294905(d).

a(n) = A294903(n) - A294905(n).

a(n) + A294902(n) = A032741(n).