A283515 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A283515

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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).

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A000169, A000203, A088790, A280257.

Sequence in context: A237341 A004833 A350746 * A333802 A229546 A373056

Adjacent sequences: A283512 A283513 A283514 * A283516 A283517 A283518

KEYWORD

nonn,more

AUTHOR

Jaroslav Krizek, Mar 10 2017

EXTENSIONS

a(7) from Giovanni Resta, Mar 10 2017

STATUS

approved