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

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

Offset

1,2

Comments

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

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A055030, A031971, A204187.

Sequence in context: A203527 A235725 A332135 * A172014 A172855 A006108

Adjacent sequences: A225575 A225576 A225577 * A225579 A225580 A225581

Keyword

easy,nonn,changed

Author

Alonso del Arte, May 10 2013

Status

approved