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%I #24 Dec 14 2017 03:45:51
%S 1,2,0,3,0,0,0,4,1,0,0,0,0,0,0,5,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,
%T 0,3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,0,0,0,0,
%U 0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0
%N Number of divisors d of n such that in binary representation d and n/d have the same number of 1's as n.
%C a(n)<=A000005(n), a(n)=A000005(n) iff n=2^k (A000079).
%C Not multiplicative. Counterexample: 441=3^2*7^2, a(441)=0, but a(3^2) = a(7^2) = 1. - _Christian G. Bower_, May 16 2005
%H G. C. Greubel, <a href="/A080024/b080024.txt">Table of n, a(n) for n = 1..5000</a>
%e Divisors of 36 = {1,2,3,4,6,9,12,18,36}, 36->100100 and also 3,6,12 have two 1's in binary notation with 36 = 3*12 = 6*6, therefore a(36)=3 (18->10010 doesn't count, as 36/18 = 2 -> 10 has only one binary 1).
%t h[n_] := Total[IntegerDigits[n, 2]]; w[n_] := DigitCount[n, 2, 1]; a[n_] := With[{hn = h[n]}, DivisorSum[ n, Boole[h[#] == hn && w[n/#] == hn]&]]; Array[a, 105] (* _Jean-François Alcover_, Dec 06 2015, adapted from PARI *)
%o (PARI) a(n) = my(hn=hammingweight(n)); sumdiv(n, d, (hammingweight(d) == hn) && (hammingweight(n/d) == hn)); \\ _Michel Marcus_, Feb 16 2015
%Y Cf. A007088, A000120, a(A080025(n))>0, a(A080026(n))=1.
%K nonn,base
%O 1,2
%A _Reinhard Zumkeller_, Jan 21 2003
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