

A225578


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


2



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

1,2


COMMENTS

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


REFERENCES

Paulo Ribemboim, The Little Book of Big Primes, New York, SpringerVerlag (1991): 17.


LINKS



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



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



