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A351198
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Sum of the 10th powers of the primes dividing n.
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11
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0, 1024, 59049, 1024, 9765625, 60073, 282475249, 1024, 59049, 9766649, 25937424601, 60073, 137858491849, 282476273, 9824674, 1024, 2015993900449, 60073, 6131066257801, 9766649, 282534298, 25937425625, 41426511213649, 60073, 9765625, 137858492873, 59049, 282476273
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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^10.
G.f.: Sum_{k>=1} prime(k)^10 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 16 2022
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MATHEMATICA
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Array[DivisorSum[#, #^10 &, PrimeQ] &, 50]
f[p_, e_] := p^10; 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
(PARI) a(n) = vecsum(apply(x->x^10, factor(n)[, 1])); \\ Michel Marcus, Feb 05 2022
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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), A351197 (k=9), this sequence (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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