A181794 Numbers n such that the number of even divisors of n is an even divisor of n.

4, 6, 10, 12, 14, 16, 20, 22, 24, 26, 28, 34, 36, 38, 44, 46, 48, 52, 58, 62, 68, 74, 76, 80, 82, 86, 90, 92, 94, 106, 112, 116, 118, 120, 122, 124, 126, 134, 142, 144, 146, 148, 150, 158, 160, 164, 166, 168, 172, 176, 178, 180, 188, 192, 194, 198, 202, 206, 208, 212, 214, 216, 218, 226, 234, 236, 240, 244, 252, 254, 256, 262, 264, 268, 272, 274, 278

Offset: 1

Author

Matthew Vandermast, Nov 14 2010

Keywords

• nonn

Comments

All terms are even, since odd numbers, even if they have an even count of divisors, don't have any even divisors.

Includes all numbers of the form A000040(m)*A001146(n).

Examples

			a(4)=12 has four even divisors (2, 4, 6, and 12), and 4 is one of those even divisors.
The number 21 is not in this sequence: it has four divisors (1, 3, 7, and 21), and 4 is not one of those divisors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

A100484 and A001749 are subsequences. A001146 and A100042 are also subsequences except for their initial terms.

See also A033950, A049439, A181795.

Programs

Mathematica

Select[Range[2, 1000, 2], EvenQ[DivisorSigma[0, #/2]] && MemberQ[Divisors[#], DivisorSigma[0, #/2]] &]
Select[Range[2, 278, 2], EvenQ[(d = DivisorSigma[0, #/2])] && Divisible[#, d] &] (* Amiram Eldar, Aug 29 2019 *)

Extensions

Verified and edited by Alonso del Arte, Nov 17 2010