A377766 - OEIS

%I #19 Jun 23 2025 14:31:44

%S 4,8,32,50,98,128,242,324,338,392,722,784,800,1058,1250,1444,2304,

%T 2312,2450,2704,2738,3600,3872,5408,5476,5618,6272,6728,7442,7688,

%U 8192,9248,11552,12482,12800,14400,14884,15488,15842,16562,16900,16928,17672,18050,19208,21632,21904,22500,23762,25088

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

%C Even terms of A037020.

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

%H Michel Marcus, <a href="/A377766/b377766.txt">Table of n, a(n) for n = 1..3000</a>

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

%t Select[2Range[13000],PrimeQ[DivisorSigma[1,#]-#] &] (* _Stefano Spezia_, Nov 08 2024 *)

%o (PARI) is_a377766(n) = !(n%2) && isprime(sigma(n)-n) \\ _Hugo Pfoertner_, Nov 07 2024

%Y Intersection of A005843 and A037020.

%Y Cf. A088827.

%K nonn,easy

%O 1,1

%A _Ophir Spector_, Nov 06 2024