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A005065
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Sum of 4th powers of primes dividing n.
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20
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0, 16, 81, 16, 625, 97, 2401, 16, 81, 641, 14641, 97, 28561, 2417, 706, 16, 83521, 97, 130321, 641, 2482, 14657, 279841, 97, 625, 28577, 81, 2417, 707281, 722, 923521, 16, 14722, 83537, 3026, 97, 1874161, 130337, 28642, 641, 2825761, 2498, 3418801, 14657, 706, 279857, 4879681, 97, 2401, 641, 83602, 28577, 7890481, 97
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OFFSET
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1,2
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COMMENTS
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Primes taken without multiplicity, e.g., 12 = 2*2*3, and a(12) = 2^4+3^4 = 97. - Harvey P. Dale, Jul 16 2014
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LINKS
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FORMULA
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Additive with a(p^e) = p^4.
(End)
G.f.: Sum_{k>=1} prime(k)^4*x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Dec 24 2018
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MAPLE
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add(d^4, d= numtheory[factorset](n)) ;
end proc;
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MATHEMATICA
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Join[{0}, Table[Total[Transpose[FactorInteger[n]][[1]]^4], {n, 2, 40}]] (* Harvey P. Dale, Jul 16 2014 *)
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PROG
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(Python)
from sympy import primefactors
def a(n): return sum(p**4 for p in primefactors(n))
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]^4); \\ Michel Marcus, Jul 11 2017
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CROSSREFS
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Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), A008472 (k=1), A005063 (k=2), A005064 (k=3), this sequence (k=4), A351193 (k=5), A351194 (k=6), A351195 (k=7), this sequence (k=8), A351197 (k=9), A351198 (k=10).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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