cp's OEIS Frontend

A231178 Let A={1,2,5,6,8,11,13,...} be the sequence of numbers k>=1 such that k+4 is evil (A001969), and let B be the complement of A. The sequence lists numbers for which the number of A-divisors equals number of B-divisors.

%I A231178 #16 Dec 23 2024 14:53:43
%S A231178 1,9,49,289,324,676,961,1369,1849,3249,4356,6084,6889,7921,8281,8836,
%T A231178 10609,11236,12769,14161,14884,15129,16129,17689,19321,21316,22500,
%U A231178 22801,24649,25281,26569,27889,28561,30276,31329,32761,39601,44944,45369,45796,47524
%N A231178 Let  A={1,2,5,6,8,11,13,...} be the sequence of numbers k>=1 such that k+4 is evil (A001969), and let B be the complement of A. The sequence lists numbers for which the number of A-divisors equals number of B-divisors.
%C A231178 All terms are perfect squares.
%H A231178 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 A231178 324 has 14 proper divisors {1,2,3,4,6,9,12,18,27,36,54,81,108,162} from which 7 from A {1,2,6,36,54,81,162} and 7 from B {3,4,9,12,18,27,108}. So 324 is in the sequence.
%t A231178 odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
%t A231178 Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+4]&]]&[Most[Divisors[#^2]]]&]^2 (* _Peter J. C. Moses_, Nov 08 2013 *)
%Y A231178 Cf. A227891, A231175, A231176, A231177, A000005, A001969.
%K A231178 nonn,base
%O A231178 1,2
%A A231178 _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 05 2013