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%I #17 Jan 04 2024 06:37:28
%S 1,4,25,100,121,289,361,529,625,841,1156,2116,2209,2500,2809,3249,
%T 3364,3481,4489,5041,5929,6241,7225,7921,10201,11236,11449,12769,
%U 12996,15625,17161,20164,21025,22201,28900,29584,30625,31329,31684,32041,36481,38809,40804
%N Let A={2,4,5,8,9,11,14,...} be the sequence of numbers k>=1 such that k+1 is evil (A001969), and let B be the complement of A. The sequence lists numbers for which number of A-divisors equals number of B-divisors.
%C This is an analog of A227891. 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=100 has 8 proper divisors {1,2,4,5,10,20,25,50} from which 4 from A, {2,4,5,50} and 4 from B, {1,10,20,25}. So 100 is in the sequence.
%t evilQ[n_] := EvenQ[DigitCount[n, 2] // First]; selQ[n_] := Length[Select[d = Most[Divisors[n]], evilQ[#+1]&]] == Length[d]/2; Select[Range[200]^2, selQ] (* _Jean-François Alcover_, Nov 05 2013 *)
%Y Cf. A227891, A000005, A001969.
%K nonn,base
%O 1,2
%A _Vladimir Shevelev_, Nov 05 2013
%E More terms from _Peter J. C. Moses_
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