A342119 - OEIS

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

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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