A259190 Primes of the form sigma(n) + sigma(n)^2 - 1.

11, 19, 41, 71, 239, 181, 811, 599, 599, 991, 1559, 419, 599, 3659, 991, 3191, 929, 2351, 2969, 2351, 1481, 3659, 3191, 9311, 1979, 2351, 8741, 2969, 14519, 14519, 3659, 9311, 20879, 4691, 16001, 9311, 20879, 38219, 13109, 19739, 9311, 34781, 16001, 14519, 32579

Offset: 1

Author

K. D. Bajpai, Jun 20 2015

Keywords

• nonn

Comments

These primes are not sorted nor unique. They are listed in the order found.

Examples

			a(2) = 19: sigma(3) + sigma(3)^2 - 1 = 4 + 16 - 1 = 19, which is prime.
a(5) = 239: sigma(8) + sigma(8)^2 - 1 = 15 + 225 - 1 = 239, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000203, A258776.

Programs

Magma

[k: n in [1..100] | IsPrime(k) where k is SumOfDivisors(n)+ SumOfDivisors(n)^2-1]; // K. D. Bajpai, Jun 20 2015

Maple

with(numtheory): A259190:= n-> (sigma(n) + sigma(n)^2-1): select(isprime,[seq((A259190 (n), n=1..500))]);

Mathematica

Select[Table[DivisorSigma[1, n] + DivisorSigma[1, n]^2 - 1, {n, 1, 10000}], PrimeQ]

PARI

for(n=1, 100, k=sigma(n)+sigma (n)^2-1; if(isprime(k), print1(k,", "))); \\ K. D. Bajpai, Jun 20 2015