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

1,1

Comments

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

Links

Table of n, a(n) for n=1..61.

Example

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

Mathematica

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

Crossrefs

Cf. A000203, A293188, A005835.

Sequence in context: A293511 A336615 A325337 * A324515 A212127 A307895

Adjacent sequences: A342116 A342117 A342118 * A342120 A342121 A342122

Keyword

nonn

Author

Metin Sariyar, Feb 28 2021

Status

approved