cp's OEIS Frontend

A231177 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.

%I A231177 #16 Dec 23 2024 14:53:43
%S A231177 1,4,9,49,196,289,961,1156,1369,1849,3249,3844,5476,6889,7921,8281,
%T A231177 10609,12769,12996,14161,15129,16129,17689,19321,22801,24649,25281,
%U A231177 26569,27889,28561,29584,31329,31684,32761,39601,42436,44944,45369,49729,51076,52441
%N A231177 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 A231177 All terms are perfect squares.
%H A231177 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 A231177 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 A231177 odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
%t A231177 Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+3]&]]&[Most[Divisors[#^2]]]&]^2 (* _Peter J. C. Moses_, Nov 08 2013 *)
%Y A231177 Cf. A227891, A231175, A231176, A000005, A000069.
%K A231177 nonn,base
%O A231177 1,2
%A A231177 _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 05 2013