A249485 Numbers n such that sigma(n) - 2 is prime.

3, 4, 8, 9, 16, 18, 25, 32, 36, 72, 121, 144, 169, 196, 200, 225, 242, 256, 338, 361, 392, 441, 484, 512, 578, 676, 729, 800, 882, 900, 961, 968, 1058, 1152, 1250, 1521, 1681, 1800, 2048, 2312, 2592, 2601, 2738, 2809, 2916, 3136, 3249, 3362, 3481, 3528, 3600

Offset: 1

Author

Jaroslav Krizek, Nov 13 2014

Keywords

• nonn
• easy

Comments

The only prime term is 3.

a(n) is a square or twice a square for n > 1. If a(n) is odd and n > 1, then a(n) must be a square. - Altug Alkan, Jul 16 2016

Examples

			Number 8 is in the sequence because sigma(8)-2 = 15-2 = 13 (prime).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000203.

Programs

Magma

[n: n in[1..100000] | IsPrime(SumOfDivisors(n)- 2)]

Mathematica

Select[Range[4000], PrimeQ[DivisorSigma[1, #] - 2] &] (* Vincenzo Librandi, Nov 14 2014 *)

PARI

for(n=1,10000,if(isprime(sigma(n)-2),print1(n,", "))) \\ Derek Orr, Nov 13 2014

PARI

list(lim)=my(v=List([3]),t); for(n=2,sqrtint(lim\1), if(isprime(sigma(t=n^2)-2), listput(v,t))); for(n=2,sqrtint(lim\2), if(isprime(sigma(t=2*n^2)-2), listput(v,t))); Set(v) \\ Charles R Greathouse IV, Jul 16 2016