%I #12 Feb 20 2021 00:36:24
%S 2,3,5,23,29
%N Primes p that divide A123373(p-1).
%e A123373 begins {4, 48, 3598, 924780, 287358579128, ...}.
%e a(1) = 2 because 2 divides A123373(1) = 4.
%e a(2) = 3 because 3 divides A123373(2) = 48.
%e a(3) = 5 because 5 divides A123373(4) = 924780.
%o (PARI) is(p) = isprime(p) && sum(j=1, p-1, sum(k=1, p-1, Mod(prime(k), p)^prime(j))) == 0; \\ _Jinyuan Wang_, Jan 16 2021
%o (Python)
%o from sympy import nextprime, prime
%o p, A122004_list = 2, []
%o while p < 10**6:
%o if 0 == sum(pow(prime(i),prime(j),p) for i in range(1,p) for j in range(1,p)) % p:
%o A122004_list.append(p)
%o p = nextprime(p) # _Chai Wah Wu_, Feb 19 2021
%Y Cf. A086787, A123373.
%K nonn,more,hard
%O 1,1
%A _Alexander Adamchuk_, Oct 14 2006
|