

A122102


Sum_{k=1..n} prime(k)^4.


12



16, 97, 722, 3123, 17764, 46325, 129846, 260167, 540008, 1247289, 2170810, 4044971, 6870732, 10289533, 15169214, 23059695, 35177056, 49022897, 69174018, 94585699, 122983940, 161934021, 209392342, 272134583, 360663864, 464724265
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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
OEIS Wiki, Sums of powers of primes divisibility sequences
V. Shevelev, Asymptotics of sum of the first n primes with a remainder term


FORMULA

Contribution by 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)^(k1)*log(log(n))).
(End)


MATHEMATICA

Table[Sum[Prime[k]^4, {k, 1, n}], {n, 1, 100}]


PROG

(PARI) a(n)=my(s); forprime(p=2, prime(n), s+=p^4); s \\ Charles R Greathouse IV, Aug 02 2013


CROSSREFS

Cf. A007504, A024450, A098999, A122103, A122127.
Sequence in context: A248883 A223902 A264580 * A214612 A014762 A045784
Adjacent sequences: A122099 A122100 A122101 * A122103 A122104 A122105


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Aug 20 2006


STATUS

approved



