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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.
3
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.
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).
Sequence in context: A161502 A279628 A241914 * A341279 A071482 A071483
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Mar 05 2019
STATUS
approved