A294901 - OEIS

%I #15 Jul 20 2023 07:01:17

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

%T 3,3,1,3,3,3,1,4,1,3,3,3,1,3,2,4,3,3,1,3,3,3,3,3,1,4,1,3,3,2,3,4,1,3,

%U 3,4,1,3,1,3,4,3,3,4,1,3,2,3,1,4,3,3,3,3,1,4,3,3,3,3,3,3,1,3,3,4,1,4,1,3,4,3,1,3,1,4,3,3,1,4,3,3,3,3,3,4

%N Number of proper divisors of n that are in A257691.

%H Antti Karttunen, <a href="/A294901/b294901.txt">Table of n, a(n) for n = 1..25000</a>

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

%F a(n) = A294903(n) - A294905(n).

%F a(n) + A294902(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 A294901(n) = sumdiv(n,d,(d<n)*A294905(d));

%Y Cf. A000120, A032741, A257691, A292257, A294902, A294903, A294904, A294905.

%Y Cf. also A294891.

%K nonn,base

%O 1,4

%A _Antti Karttunen_, Nov 10 2017