A231180 Let A={2,3,6,8,9,11,14,...} be the sequence of numbers k>=1 such that k+5 is odious (A000069). 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, 9, 16, 36, 121, 144, 289, 441, 484, 529, 1156, 1369, 1600, 1764, 2025, 2116, 2209, 3249, 3481, 4624, 5041, 5476, 6241, 6889, 7056, 7569, 7921, 8100, 8464, 8649, 8836, 11449, 12321, 12769, 12996, 13924, 14641, 15129, 16641, 20164, 24336, 24649, 24964

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

All terms are perfect squares.

Examples

			n=16 has 4 proper divisors {1,2,4,8} from which 2 from A {2,8} and 2 from B {1,4}. So 16 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Vladimir Shevelev, A set of sequences of perfect squares

Crossrefs

Cf. A227891, A231175, A231176, A092498, A231178, A000005, A000069.

Programs

Mathematica

odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]];
Select[Range[200],0==Length[#]-2Length[Select[#,odiousQ[#+5]&]]&[Most[Divisors[#^2]]]&]^2 (* Peter J. C. Moses, Nov 08 2013 *)