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A351197
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Sum of the 9th powers of the primes dividing n.
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11
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0, 512, 19683, 512, 1953125, 20195, 40353607, 512, 19683, 1953637, 2357947691, 20195, 10604499373, 40354119, 1972808, 512, 118587876497, 20195, 322687697779, 1953637, 40373290, 2357948203, 1801152661463, 20195, 1953125, 10604499885, 19683, 40354119, 14507145975869, 1973320, 26439622160671, 512, 2357967374
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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^9.
G.f.: Sum_{k>=1} prime(k)^9 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 16 2022
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MATHEMATICA
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Array[DivisorSum[#, #^9 &, PrimeQ] &, 50]
f[p_, e_] := p^9; 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), A351196 (k=8), this sequence (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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