A338472 - OEIS

%I #21 Dec 23 2020 07:31:24

%S 3,109,14519,2024592291,1536463613637,2449395996564189425,

%T 4686662617019462175259,33724155827962966577589860263,

%U 2606282943971359343146382147809434583605,15159042500551578738018590862773479717960671,6576976543997974825092367662248938303820921894460988333

%N (1 + Sum_{k(even)=2..p-1} 2*k^(p-1))/p as p runs through the odd primes.

%C Conjecture: (1 + Sum_{k(even)=2..p-1} 2*k^(p-1))/p is an integer iff p is an odd prime.

%t a[n_] := Module[{p = Prime[n + 1]}, (1 + 2 * Sum[k^(p - 1), {k, 2, p - 1, 2}])/p]; Array[a, 11] (* _Amiram Eldar_, Oct 29 2020 *)

%o (PARI) a(n) = my(p=prime(n+1)); (1 + sum(k=1, (p-1)\2, 2*(2*k)^(p-1)))/p; \\ _Michel Marcus_, Oct 29 2020

%Y Cf. A055030.

%K nonn

%O 1,1

%A _Davide Rotondo_, Oct 29 2020