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A292257 a(n) is the total number of 1's in binary expansion of all proper divisors of n.

%I A292257 #16 Oct 11 2024 19:59:07
%S A292257 0,1,1,2,1,4,1,3,3,4,1,7,1,5,5,4,1,8,1,7,6,5,1,10,3,5,5,9,1,14,1,5,6,
%T A292257 4,6,13,1,5,6,10,1,15,1,9,11,6,1,13,4,9,5,9,1,14,6,13,6,6,1,23,1,7,11,
%U A292257 6,6,14,1,7,7,15,1,18,1,5,12,9,7,16,1,13,9,5,1,24,5,6,7,13,1,26,7,11,8,7,6,16,1,11,10,15,1,14,1,13,18
%N A292257 a(n) is the total number of 1's in binary expansion of all proper divisors of n.
%C A292257 If a(n) == A000120(n), then n is in A175522, if a(n) < A000120(n), then n is in A175524, and if a(n) > A000120(n), then n is in A175526.
%H A292257 Antti Karttunen, <a href="/A292257/b292257.txt">Table of n, a(n) for n = 1..16384</a>
%H A292257 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%F A292257 a(n) = Sum_{d|n, d<n} A000120(d).
%F A292257 a(n) = A093653(n) - A000120(n).
%F A292257 a(n) = A192895(n) + A000120(n).
%F A292257 a(n) = A001222(A293214(n)).
%F A292257 A000035(a(n)) = A000035(A290090(n)). [Parity-wise equivalent with A290090.]
%t A292257 a[n_] := DivisorSum[n, DigitCount[#, 2, 1] &, # < n &]; Array[a, 100] (* _Amiram Eldar_, Jul 20 2023 *)
%t A292257 Table[Total[Flatten[IntegerDigits[#,2]&/@Most[Divisors[n]]]],{n,120}] (* _Harvey P. Dale_, Oct 11 2024 *)
%o A292257 (PARI) A292257(n) = sumdiv(n,d,(d<n)*hammingweight(d));
%Y A292257 Cf. A000120, A093653, A175522, A175524, A175526, A192895, A290090, A293214.
%K A292257 nonn,base
%O A292257 1,4
%A A292257 _Antti Karttunen_, Oct 04 2017