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A294901 Number of proper divisors of n that are in A257691.

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%I A294901 #15 Jul 20 2023 07:01:17
%S A294901 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 A294901 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 A294901 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 A294901 Number of proper divisors of n that are in A257691.
%H A294901 Antti Karttunen, <a href="/A294901/b294901.txt">Table of n, a(n) for n = 1..25000</a>
%F A294901 a(n) = Sum_{d|n, d<n} A294905(d).
%F A294901 a(n) = A294903(n) - A294905(n).
%F A294901 a(n) + A294902(n) = A032741(n).
%t A294901 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 A294901 (PARI)
%o A294901 A292257(n) = sumdiv(n,d,(d<n)*hammingweight(d));
%o A294901 A294905(n) = (A292257(n) <= hammingweight(n));
%o A294901 A294901(n) = sumdiv(n,d,(d<n)*A294905(d));
%Y A294901 Cf. A000120, A032741, A257691, A292257, A294902, A294903, A294904, A294905.
%Y A294901 Cf. also A294891.
%K A294901 nonn,base
%O A294901 1,4
%A A294901 _Antti Karttunen_, Nov 10 2017