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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.
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%I #18 Jan 04 2024 06:36:00

%S 1,4,25,36,100,121,289,361,529,625,841,1156,1764,2116,2209,2500,2809,

%T 3249,3364,3481,4489,5041,5929,6241,7225,7396,7921,10201,11236,11449,

%U 12769,12996,15625,17161,20164,21025,22201,27556,28900,30276,30625,31329,31684

%N 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 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 {1,4,10,25} and 4 from B {2,5,20,50}. So 100 is in the sequence.

%t odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];

%t Select[Range[100],0==Length[#]-2Length[Select[#,odiousQ[#+2]&]]&[Most[Divisors[#^2]]]&]^2 (* _Peter J. C. Moses_, Nov 08 2013 *)

%Y Cf. A000005, A001969, A227891, A231175.

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Nov 05 2013

%E More terms from _Peter J. C. Moses_, Nov 05 2013