A283515 Numbers k such that sigma(k^(k-1)) is a prime.

2, 3, 4, 16, 19, 31, 7547

Offset: 1

Author

Jaroslav Krizek, Mar 10 2017

Keywords

• nonn
• more

Comments

sigma(k) is the sum of the divisors of k (A000203).

Numbers k such that A000203(A000169(k)) is a prime.

a(8) > 10^4.

Corresponding values of k^(k-1): 2, 9, 64, 1152921504606846976, ...

Corresponding values of sigma(k^(k-1)): 3, 13, 127, 2305843009213693951, ...

Subsequence of A280257 (numbers k such that tau(k^(k-1)) is prime).

Prime terms are in A088790.

For k < 1000, sigma(k^(k+1)) is prime only for k = 5: sigma(5^6) = sigma(15625) = 19531 (prime).

Examples

			sigma(4^3) = sigma(64) = 127 (prime).
		

Crossrefs

Cf. A000169, A000203, A088790, A280257.

Programs

Magma

[n: n in [1..500] | IsPrime(SumOfDivisors(n^(n-1)))];

Mathematica

fQ[n_] := PrimeQ[DivisorSigma[1, n^(n - 1)]]; Select[Range@1000, fQ] (* Robert G. Wilson v, Mar 10 2017 *)

PARI

isok(n) = isprime(sigma(n^(n-1))); \\ Michel Marcus, Mar 10 2017

Extensions

a(7) from Giovanni Resta, Mar 10 2017