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A231180 Let A={2,3,6,8,9,11,14,...} be the sequence of numbers k>=1 such that k+5 is odious (A000069). 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 A231180 #24 Dec 23 2024 14:53:43
%S A231180 1,4,9,16,36,121,144,289,441,484,529,1156,1369,1600,1764,2025,2116,
%T A231180 2209,3249,3481,4624,5041,5476,6241,6889,7056,7569,7921,8100,8464,
%U A231180 8649,8836,11449,12321,12769,12996,13924,14641,15129,16641,20164,24336,24649,24964
%N A231180 Let A={2,3,6,8,9,11,14,...} be the sequence of numbers k>=1 such that k+5 is odious (A000069). 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 A231180 All terms are perfect squares.
%H A231180 Amiram Eldar, <a href="/A231180/b231180.txt">Table of n, a(n) for n = 1..10000</a>
%H A231180 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 A231180 n=16 has 4 proper divisors {1,2,4,8} from which 2 from A {2,8} and 2 from B {1,4}. So 16 is in the sequence.
%t A231180 odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
%t A231180 Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+5]&]]&[Most[Divisors[#^2]]]&]^2 (* _Peter J. C. Moses_, Nov 08 2013 *)
%Y A231180 Cf. A227891, A231175, A231176, A092498, A231178, A000005, A000069.
%K A231180 nonn,base
%O A231180 1,2
%A A231180 _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 05 2013