A294902 - OEIS

%I #11 Jul 20 2023 07:01:21

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

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

%U 0,3,0,8,0,0,1,2,0,3,0,6,2,0,0,7,0,0,0,4,0,7,0,2,0,0,0,8,0,2,2,4,0,3,0,4,3,0,0,8,0,3,0,6,0,3,0,2,2,0,0,11

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

%H Antti Karttunen, <a href="/A294902/b294902.txt">Table of n, a(n) for n = 1..25000</a>

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

%F a(n) = A294904(n) + A294905(n) - 1.

%F a(n) + A294901(n) = A032741(n).

%t q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] > 2 * DigitCount[n, 2, 1]; a[n_] := DivisorSum[n, 1 &, # < n && 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 A294902(n) = sumdiv(n,d,(d<n)*(0==A294905(d)));

%Y Cf. A000120, A032741, A175526, A292257, A294901, A294903, A294904, A294905.

%Y Cf. also A294892.

%K nonn,base

%O 1,12

%A _Antti Karttunen_, Nov 10 2017