A324393 - OEIS

%I #17 Dec 04 2020 09:21:59

%S 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,

%T 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,

%U 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

%N 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.

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

%H Antti Karttunen, <a href="/A324393/b324393.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

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

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

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

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

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

%Y Cf. also A093653, A192895, A266342, A292257.

%K nonn,base

%O 1,9

%A _Antti Karttunen_, Mar 05 2019