A225578 - OEIS

%I #17 Sep 25 2024 09:54:57

%S 1,5,354,67171,14914341925,13421957361110,28101527071305611528,

%T 60182438244917445266889,525344775209112229247070397995,

%U 51296981152155330485450049059398345004638,319099356359853147544285512855368258519442575

%N Sum of first (prime(n) - 1) (prime(n) - 1)th powers.

%C It follows from Fermat's little theorem that a(n) is congruent to -1 mod the n-th prime.

%D R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section A17.

%D Paulo Ribemboim, The Little Book of Big Primes, New York, Springer-Verlag (1991): 17.

%H Seiichi Manyama, <a href="/A225578/b225578.txt">Table of n, a(n) for n = 1..76</a>

%F a(n) = Sum_{i=1..prime(n)-1} i^(prime(n) - 1).

%e a(2) = 5 because, since 3 is the second prime, we have 1^2 + 2^2 = 1 + 4 = 5.

%e a(3) = 354 because, since 5 is the third prime, we have 1^4 + 2^4 + 3^4 + 4^4 = 1 + 4 + 81 + 256 = 354.

%t Table[Sum[i^(Prime[n] - 1), {i, Prime[n] - 1}], {n, 15}]

%Y Cf. A055030, A031971, A204187.

%K easy,nonn

%O 1,2

%A _Alonso del Arte_, May 10 2013