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A351196
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Sum of the 8th powers of the primes dividing n.
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7
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0, 256, 6561, 256, 390625, 6817, 5764801, 256, 6561, 390881, 214358881, 6817, 815730721, 5765057, 397186, 256, 6975757441, 6817, 16983563041, 390881, 5771362, 214359137, 78310985281, 6817, 390625, 815730977, 6561, 5765057, 500246412961, 397442, 852891037441, 256
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{p|n, p prime} p^8.
G.f.: Sum_{k>=1} prime(k)^8 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 16 2022
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MATHEMATICA
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Array[DivisorSum[#, #^8 &, PrimeQ] &, 50]
f[p_, e_] := p^8; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 20 2022 *)
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PROG
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(Python)
from sympy import primefactors
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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), A005065 (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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STATUS
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approved
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