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%I #27 Jun 20 2022 04:21:07
%S 0,1024,59049,1024,9765625,60073,282475249,1024,59049,9766649,
%T 25937424601,60073,137858491849,282476273,9824674,1024,2015993900449,
%U 60073,6131066257801,9766649,282534298,25937425625,41426511213649,60073,9765625,137858492873,59049,282476273
%N Sum of the 10th powers of the primes dividing n.
%H Seiichi Manyama, <a href="/A351198/b351198.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{p|n, p prime} p^10.
%F G.f.: Sum_{k>=1} prime(k)^10 * x^prime(k) / (1 - x^prime(k)). - _Ilya Gutkovskiy_, Feb 16 2022
%F Additive with a(p^e) = p^10. - _Amiram Eldar_, Jun 20 2022
%t Array[DivisorSum[#, #^10 &, PrimeQ] &, 50]
%t f[p_, e_] := p^10; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 20 2022 *)
%o (Python)
%o from sympy import primefactors
%o def A351198(n): return sum(p**10 for p in primefactors(n)) # _Chai Wah Wu_, Feb 04 2022
%o (PARI) a(n) = vecsum(apply(x->x^10, factor(n)[, 1])); \\ _Michel Marcus_, Feb 05 2022
%Y 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).
%Y Cf. A030629 (p^10).
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Feb 04 2022
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