A324392 a(n) is the number of divisors d of n such that A000120(d) divides n, where A000120(d) gives the binary weight of d.

1, 2, 1, 3, 1, 4, 1, 4, 1, 4, 1, 6, 1, 2, 1, 5, 1, 6, 1, 6, 3, 2, 1, 8, 1, 2, 1, 3, 1, 6, 1, 6, 2, 4, 1, 9, 1, 2, 2, 8, 1, 8, 1, 3, 1, 2, 1, 10, 1, 4, 1, 3, 1, 6, 2, 4, 2, 2, 1, 12, 1, 2, 3, 7, 1, 8, 1, 6, 2, 4, 1, 12, 1, 2, 2, 3, 1, 6, 1, 10, 2, 2, 1, 12, 1, 2, 1, 4, 1, 8, 1, 6, 1, 2, 1, 12, 1, 2, 2, 6, 1, 6, 1, 4, 4

Offset: 1

Author

Antti Karttunen, Mar 05 2019

Keywords

• nonn
• base

Comments

Number of such positive integers k that both k and A000120(k) [the Hamming weight of k] divide n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000005, A000120, A324393.

Cf. also A093653, A192895, A266342, A292257.

Programs

Mathematica

a[n_] := DivisorSum[n, 1 &, Divisible[n, DigitCount[#, 2, 1]] &]; Array[a, 100] (* Amiram Eldar, Dec 04 2020 *)

PARI

A324392(n) = sumdiv(n, d, !(n%hammingweight(d)));

Formula

a(n) = Sum_{d|n} [A000120(d) does divide n], where [ ] is the Iverson bracket.

a(n) = A000005(n) - A324393(n).

a(p) = 1 for all odd primes p.