A231176 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.

1, 4, 25, 36, 100, 121, 289, 361, 529, 625, 841, 1156, 1764, 2116, 2209, 2500, 2809, 3249, 3364, 3481, 4489, 5041, 5929, 6241, 7225, 7396, 7921, 10201, 11236, 11449, 12769, 12996, 15625, 17161, 20164, 21025, 22201, 27556, 28900, 30276, 30625, 31329, 31684

Offset: 1

Author

Vladimir Shevelev, Nov 05 2013

Keywords

• nonn
• base

Comments

An analog of A227891. All terms are perfect squares.

Examples

			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.
		

Links

• Vladimir Shevelev, A set of sequences of perfect squares

Crossrefs

Cf. A000005, A001969, A227891, A231175.

Programs

Mathematica

odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
Select[Range[100],0==Length[#]-2Length[Select[#,odiousQ[#+2]&]]&[Most[Divisors[#^2]]]&]^2 (* Peter J. C. Moses, Nov 08 2013 *)

Extensions

More terms from Peter J. C. Moses, Nov 05 2013