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A283515 Numbers n such that sigma(n^(n-1)) is a prime. 0
2, 3, 4, 16, 19, 31, 7547 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

a(8) > 10^4.

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

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

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

Prime terms are in A088790.

For n < 1000; sigma(n^(n+1)) is prime only for n = 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 A343494

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

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)