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%I #15 Jan 04 2024 10:56:45
%S 1,4,9,49,196,289,961,1156,1369,1849,3249,3844,5476,6889,7921,8281,
%T 10609,12769,12996,14161,15129,16129,17689,19321,22801,24649,25281,
%U 26569,27889,28561,29584,31329,31684,32761,39601,42436,44944,45369,49729,51076,52441
%N Let A = {1,4,5,8,10,11,13,...} be the sequence of numbers k>=1 such that k+3 is odious (A000069), and let B be the complement of A. The sequence lists the numbers for which the number of A-divisors equals the number of B-divisors.
%C All terms are perfect squares.
%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-October/011800.html">A set of sequences of perfect squares</a>
%e n=196 has 8 proper divisors {1,2,4,7,14,28,49,98} from which 4 from A {1,4,28,49} and 4 from B {2,7,14,98}. So 196 is in the sequence.
%t odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
%t Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+3]&]]&[Most[Divisors[#^2]]]&]^2 (* _Peter J. C. Moses_, Nov 08 2013 *)
%Y Cf. A227891, A231175, A231176, A000005, A000069.
%K nonn,base
%O 1,2
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 05 2013
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