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A122102
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a(n) = Sum_{k=1..n} prime(k)^4.
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16
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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, 577275146, 708354747, 849512908
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OFFSET
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1,1
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COMMENTS
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a(n) is prime for n = {2,32,90,110,134,152,168,180,194,...} = A122127.
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LINKS
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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
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FORMULA
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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)
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MAPLE
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seq(add(ithprime(k)^4, k=1..n), n=1..30); # G. C. Greubel, Oct 02 2019
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MATHEMATICA
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Table[Sum[Prime[k]^4, {k, 1, n}], {n, 1, 100}]
Accumulate[Prime[Range[30]]^4] (* Harvey P. Dale, Aug 07 2021 *)
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PROG
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(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
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CROSSREFS
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Cf. A007504, A024450, A098999, A122103, A122127.
Partial sums of A030514.
Sequence in context: A248883 A223902 A264580 * A214612 A283545 A297684
Adjacent sequences: A122099 A122100 A122101 * A122103 A122104 A122105
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk, Aug 20 2006
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STATUS
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approved
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