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A231176 Let A={1,3,4,7,8,10,13,15,...} be the sequence of numbers k>=1 such that k+2 is evil (A001969), let B be the complement of A. The sequence lists numbers for which the number of A-divisors equals the number of B-divisors.

%I A231176 #19 Dec 23 2024 14:53:43
%S A231176 1,4,25,36,100,121,289,361,529,625,841,1156,1764,2116,2209,2500,2809,
%T A231176 3249,3364,3481,4489,5041,5929,6241,7225,7396,7921,10201,11236,11449,
%U A231176 12769,12996,15625,17161,20164,21025,22201,27556,28900,30276,30625,31329,31684
%N A231176 Let A={1,3,4,7,8,10,13,15,...} be the sequence of numbers k>=1 such that k+2 is evil (A001969), let B be the complement of A. The sequence lists numbers for which the number of A-divisors equals the number of B-divisors.
%C A231176 An analog of A227891. All terms are perfect squares.
%H A231176 Vladimir Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/011800.html">A set of sequences of perfect squares</a>
%e A231176 n=100 has 8 proper divisors {1,2,4,5,10,20,25,50} from which 4 from A {1,4,10,25} and 4 from B {2,5,20,50}. So 100 is in the sequence.
%t A231176 odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
%t A231176 Select[Range[100],0==Length[#]-2Length[Select[#,odiousQ[#+2]&]]&[Most[Divisors[#^2]]]&]^2 (* _Peter J. C. Moses_, Nov 08 2013 *)
%Y A231176 Cf. A000005, A001969, A227891, A231175.
%K A231176 nonn,base
%O A231176 1,2
%A A231176 _Vladimir Shevelev_, Nov 05 2013
%E A231176 More terms from _Peter J. C. Moses_, Nov 05 2013