A377766 Even numbers whose sum of proper (or aliquot) divisors is a prime.

4, 8, 32, 50, 98, 128, 242, 324, 338, 392, 722, 784, 800, 1058, 1250, 1444, 2304, 2312, 2450, 2704, 2738, 3600, 3872, 5408, 5476, 5618, 6272, 6728, 7442, 7688, 8192, 9248, 11552, 12482, 12800, 14400, 14884, 15488, 15842, 16562, 16900, 16928, 17672, 18050, 19208, 21632, 21904, 22500, 23762, 25088

Offset: 1

Author

Ophir Spector, Nov 06 2024

Keywords

• nonn
• easy

Comments

Even terms of A037020.

Numbers from A088827 (2n^2 or 4n^2) are the only aliquot sum transition from even to odd.

Examples

			The aliquot divisors of 32 are 1, 2, 4, 8 and 16, whose sum is 31, a prime, so 32 is a term.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..3000

Crossrefs

Intersection of A005843 and A037020.

Cf. A088827.

Programs

Mathematica

Select[2Range[13000],PrimeQ[DivisorSigma[1,#]-#] &] (* Stefano Spezia, Nov 08 2024 *)

PARI

is_a377766(n) = !(n%2) && isprime(sigma(n)-n) \\ Hugo Pfoertner, Nov 07 2024