|
%I #18 Jan 16 2023 21:41:36
%S 2,3,4,16,19,31,7547
%N Numbers k such that sigma(k^(k-1)) is a prime.
%C sigma(k) is the sum of the divisors of k (A000203).
%C Numbers k such that A000203(A000169(k)) is a prime.
%C a(8) > 10^4.
%C Corresponding values of k^(k-1): 2, 9, 64, 1152921504606846976, ...
%C Corresponding values of sigma(k^(k-1)): 3, 13, 127, 2305843009213693951, ...
%C Subsequence of A280257 (numbers k such that tau(k^(k-1)) is prime).
%C Prime terms are in A088790.
%C For k < 1000, sigma(k^(k+1)) is prime only for k = 5: sigma(5^6) = sigma(15625) = 19531 (prime).
%e sigma(4^3) = sigma(64) = 127 (prime).
%t fQ[n_] := PrimeQ[DivisorSigma[1, n^(n - 1)]]; Select[Range@1000, fQ] (* _Robert G. Wilson v_, Mar 10 2017 *)
%o (Magma) [n: n in [1..500] | IsPrime(SumOfDivisors(n^(n-1)))]
%o (PARI) isok(n) = isprime(sigma(n^(n-1))); \\ _Michel Marcus_, Mar 10 2017
%Y Cf. A000169, A000203, A088790, A280257.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Mar 10 2017
%E a(7) from _Giovanni Resta_, Mar 10 2017
| 