A231175 Let A={2,4,5,8,9,11,14,...} be the sequence of numbers k>=1 such that k+1 is evil (A001969), and let B be the complement of A. The sequence lists numbers for which number of A-divisors equals number of B-divisors.

1, 4, 25, 100, 121, 289, 361, 529, 625, 841, 1156, 2116, 2209, 2500, 2809, 3249, 3364, 3481, 4489, 5041, 5929, 6241, 7225, 7921, 10201, 11236, 11449, 12769, 12996, 15625, 17161, 20164, 21025, 22201, 28900, 29584, 30625, 31329, 31684, 32041, 36481, 38809, 40804

Offset: 1

Author

Vladimir Shevelev, Nov 05 2013

Keywords

• nonn
• base

Comments

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

Links

• Vladimir Shevelev, A set of sequences of perfect squares

Crossrefs

Cf. A227891, A000005, A001969.

Programs

Mathematica

evilQ[n_] := EvenQ[DigitCount[n, 2] // First]; selQ[n_] := Length[Select[d = Most[Divisors[n]], evilQ[#+1]&]] == Length[d]/2; Select[Range[200]^2, selQ] (* Jean-François Alcover, Nov 05 2013 *)

Extensions

More terms from Peter J. C. Moses