OFFSET
1,1
COMMENTS
LINKS
FORMULA
a(n) = sum(k = 1 .. n, prime(k)^5).
a(n) = 1/6*n^6*log(n)^5 + O(n^6*log(n)^4*log(log(n))). The proof is similar to proof for A007504(n) (see link of Shevelev). For a generalization, see comment in A122102. - Vladimir Shevelev, Aug 14 2013
EXAMPLE
a(2) = 275 because the first two primes are 2 and 3, the fifth powers of which are 32 and 243, and 32 + 243 = 275.
a(3) = 3400, because the third prime is 5, its fifth power if 3125 and 275 + 3125 = 3400.
MATHEMATICA
Table[Sum[Prime[k]^5, {k, n}], {n, 100}]
PROG
(PARI) a(n)=sum(i=1, n, prime(i)) \\ Charles R Greathouse IV, Nov 30 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, Aug 20 2006
STATUS
approved