A342119 Numbers k with property that if k has m divisors, there are m/2 divisors of k whose sum is k.

2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 23, 24, 29, 30, 31, 37, 40, 41, 42, 43, 47, 48, 53, 54, 59, 60, 61, 67, 71, 72, 73, 79, 80, 83, 84, 89, 90, 96, 97, 101, 103, 107, 108, 109, 112, 113, 120, 126, 127, 131, 132, 137, 139, 140, 149, 150, 151, 156, 157, 160, 162

Offset: 1

Author

Metin Sariyar, Feb 28 2021

Keywords

• nonn

Comments

All primes and all numbers of the form 3*2^k (k>1) are terms.

Examples

			40 is a term because it has 8 divisors and 2+8+10+20 = 40.
		

Crossrefs

Cf. A000203, A293188, A005835.

Programs

Mathematica

Select[Range[160], EvenQ[(d = DivisorSigma[0, #])] && MemberQ[Plus @@@ Subsets[Divisors[#], {d/2}], #] &] (* Amiram Eldar, Feb 28 2021 *)