A249763 - OEIS

%I #27 Sep 08 2022 08:46:10

%S 1,2,8,18,49,72,98,128,196,200,242,288,361,392,441,676,968,1369,1521,

%T 1568,1764,1800,2178,2401,2450,2888,3200,3362,3528,3969,4232,5000,

%U 5476,5776,5929,6241,6272,7056,7200,7442,7688,7938,8281,8450,8649,9025,9522,9604

%N Numbers k such that sigma(k) + 2 is prime.

%C Except for 2, subsequence of nonprime numbers (A018252).

%C All odd terms are squares. - _Michel Marcus_, Dec 09 2014

%C Each term is either a square or twice a square. - _Robert Israel_, Dec 09 2014

%H Robert Israel, <a href="/A249763/b249763.txt">Table of n, a(n) for n = 1..10000</a>

%e 8 is in the sequence because sigma(8)+2 = 15+2 = 17 (prime).

%p N:= 10^5: # to get all terms <= N

%p select(n -> isprime(numtheory:-sigma(n)+2), {seq(i^2,i=1..floor(sqrt(N))), seq(2*i^2,i=1..floor(sqrt(N/2)))} );

%p # if using Maple 11 or earlier, uncomment the next line

%p # sort(convert(%,list)); # _Robert Israel_, Dec 09 2014

%t Select[Range[10000], PrimeQ[DivisorSigma[1, #] + 2] &] (* _Vincenzo Librandi_, Nov 14 2014 *)

%o (Magma) [n: n in[1..100000] | IsPrime(SumOfDivisors(n) + 2)]

%o (PARI) for(n=1,10^5,if(isprime(sigma(n)+2),print1(n,", "))) \\ _Derek Orr_, Nov 13 2014

%Y Cf. A000040, A000203, A018252.

%K nonn,easy

%O 1,2

%A _Jaroslav Krizek_, Nov 13 2014