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.

1, 4, 9, 49, 196, 289, 961, 1156, 1369, 1849, 3249, 3844, 5476, 6889, 7921, 8281, 10609, 12769, 12996, 14161, 15129, 16129, 17689, 19321, 22801, 24649, 25281, 26569, 27889, 28561, 29584, 31329, 31684, 32761, 39601, 42436, 44944, 45369, 49729, 51076, 52441

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

All terms are perfect squares.

Examples

			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.
		

Links

• Vladimir Shevelev, A set of sequences of perfect squares

Crossrefs

Cf. A227891, A231175, A231176, A000005, A000069.

Programs

Mathematica

odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+3]&]]&[Most[Divisors[#^2]]]&]^2 (* Peter J. C. Moses, Nov 08 2013 *)