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.

1, 9, 49, 289, 324, 676, 961, 1369, 1849, 3249, 4356, 6084, 6889, 7921, 8281, 8836, 10609, 11236, 12769, 14161, 14884, 15129, 16129, 17689, 19321, 21316, 22500, 22801, 24649, 25281, 26569, 27889, 28561, 30276, 31329, 32761, 39601, 44944, 45369, 45796, 47524

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Nov 05 2013

Keywords

• nonn
• base

Comments

All terms are perfect squares.

Examples

			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.
		

Links

• Vladimir Shevelev, A set of sequences of perfect squares

Crossrefs

Cf. A227891, A231175, A231176, A231177, A000005, A001969.

Programs

Mathematica

odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+4]&]]&[Most[Divisors[#^2]]]&]^2 (* Peter J. C. Moses, Nov 08 2013 *)