A324393 a(n) is the number of such divisors d of n that A000120(d) does not divide n, where A000120(d) gives the binary weight of d.

0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 2, 3, 3, 1, 2, 1, 0, 2, 0, 3, 0, 1, 2, 2, 0, 1, 0, 1, 3, 5, 2, 1, 0, 2, 2, 3, 3, 1, 2, 2, 4, 2, 2, 1, 0, 1, 2, 3, 0, 3, 0, 1, 0, 2, 4, 1, 0, 1, 2, 4, 3, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 3, 4, 1, 4, 3, 0, 3, 2, 3, 0, 1, 4, 4, 3, 1, 2, 1, 4, 4

Offset

1,9

Comments

Number of such positive integers k that divide n but A000120(k) [the Hamming weight of k] does not divide n.

Links

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

Index entries for sequences related to binary expansion of n

Formula

a(n) = Sum_{d|n} [A000120(d) does not divide n], where [ ] is the Iverson bracket.

a(n) = A000005(n) - A324392(n).

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

Mathematica

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

Prog

(PARI) A324393(n) = sumdiv(n, d, !!(n%hammingweight(d)));

Crossrefs

Cf. A000005, A000120, A324392, A306263 (positions of zeros).

Cf. also A093653, A192895, A266342, A292257.

Sequence in context: A161502 A279628 A241914 * A341279 A071482 A071483

Adjacent sequences: A324390 A324391 A324392 * A324394 A324395 A324396

Keyword

nonn,base

Author

Antti Karttunen, Mar 05 2019

Status

approved