A225578 Sum of first (prime(n) - 1) (prime(n) - 1)th powers.

1, 5, 354, 67171, 14914341925, 13421957361110, 28101527071305611528, 60182438244917445266889, 525344775209112229247070397995, 51296981152155330485450049059398345004638, 319099356359853147544285512855368258519442575

Offset: 1

Author

Alonso del Arte, May 10 2013

Keywords

• easy
• nonn

Comments

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

Examples

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

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section A17.
• Paulo Ribemboim, The Little Book of Big Primes, New York, Springer-Verlag (1991): 17.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..76

Crossrefs

Cf. A055030, A031971, A204187.

Programs

Mathematica

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

Formula

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