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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A000005, A000120, A324393.

Cf. also A093653, A192895, A266342, A292257.

Sequence in context: A328578 A094741 A285577 * A340273 A029234 A102613

Adjacent sequences:  A324389 A324390 A324391 * A324393 A324394 A324395

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Mar 05 2019

STATUS

approved

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Last modified January 20 19:03 EST 2022. Contains 350472 sequences. (Running on oeis4.)