OFFSET
1,1
COMMENTS
a(n) is prime for n = {2,32,90,110,134,152,168,180,194,...} = A122127.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
From Vladimir Shevelev, Aug 02 2013: (Start)
a(n) = 0.2*n^5*log(n)^4 + O(n^5*log(n)^3*log(log(n))). The proof is similar to proof for A007504(n) (see link of Shevelev).
A generalization: Sum_{i=1..n} prime(i)^k = 1/(k+1)*n^(k+1)*log(n)^k + O(n^(k+1)*log(n)^(k-1)*log(log(n))).
(End)
MAPLE
seq(add(ithprime(k)^4, k=1..n), n=1..30); # G. C. Greubel, Oct 02 2019
MATHEMATICA
Table[Sum[Prime[k]^4, {k, 1, n}], {n, 1, 100}]
Accumulate[Prime[Range[30]]^4] (* Harvey P. Dale, Aug 07 2021 *)
PROG
(PARI) a(n)=my(s); forprime(p=2, prime(n), s+=p^4); s \\ Charles R Greathouse IV, Aug 02 2013
(Magma) [&+[NthPrime(k)^4: k in [1..n]]: n in [1..30]]; // G. C. Greubel, Oct 02 2019
(Sage) [sum(nth_prime(k)^4 for k in (1..n)) for n in (1..30)] # G. C. Greubel, Oct 02 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Aug 20 2006
STATUS
approved