A294904 - OEIS

%I #10 Jul 20 2023 07:01:27

%S 0,0,0,1,0,1,0,2,1,1,0,3,0,1,1,3,0,3,0,3,1,1,0,5,0,1,2,3,0,4,0,4,1,1,

%T 1,6,0,1,1,5,0,4,0,3,3,1,0,7,1,2,1,3,0,5,1,5,1,1,0,8,0,1,3,5,1,4,0,3,

%U 1,4,0,9,0,1,2,3,1,4,0,7,3,1,0,8,1,1,1,5,0,8,1,3,1,1,0,9,0,3,3,5,0,4,0,5,4,1,0,9,0,4,0,7,0,4,1,3,3,1,0,12

%N Number of divisors of n that are in A175526.

%C Number of terms of A175526 that divide n.

%H Antti Karttunen, <a href="/A294904/b294904.txt">Table of n, a(n) for n = 1..25000</a>

%F a(n) = Sum_{d|n} (1-A294905(d)).

%F a(n) = 1 + (A294902(n)-A294905(n)).

%F a(n) + A294903(n) = A000005(n).

%t q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] > 2 * DigitCount[n, 2, 1]; a[n_] := DivisorSum[n, 1 &, q[#] &]; Array[a, 100] (* _Amiram Eldar_, Jul 20 2023 *)

%o (PARI)

%o A292257(n) = sumdiv(n,d,(d<n)*hammingweight(d));

%o A294905(n) = (A292257(n) <= hammingweight(n));

%o A294904(n) = sumdiv(n,d,(0==A294905(d)));

%Y Cf. A000120, A175526, A292257, A294901, A294902, A294903, A294905.

%Y Cf. also A294894.

%K nonn,base

%O 1,8

%A _Antti Karttunen_, Nov 10 2017