This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351196 #23 Jun 22 2024 18:38:45
%S A351196 0,256,6561,256,390625,6817,5764801,256,6561,390881,214358881,6817,
%T A351196 815730721,5765057,397186,256,6975757441,6817,16983563041,390881,
%U A351196 5771362,214359137,78310985281,6817,390625,815730977,6561,5765057,500246412961,397442,852891037441,256
%N A351196 Sum of the 8th powers of the primes dividing n.
%C A351196 Inverse Möbius transform of n^8 * c(n), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 22 2024
%H A351196 Seiichi Manyama, <a href="/A351196/b351196.txt">Table of n, a(n) for n = 1..10000</a>
%F A351196 a(n) = Sum_{p|n, p prime} p^8.
%F A351196 G.f.: Sum_{k>=1} prime(k)^8 * x^prime(k) / (1 - x^prime(k)). - _Ilya Gutkovskiy_, Feb 16 2022
%F A351196 Additive with a(p^e) = p^8. - _Amiram Eldar_, Jun 20 2022
%F A351196 a(n) = Sum_{d|n} d^8 * c(d), where c = A010051. - _Wesley Ivan Hurt_, Jun 22 2024
%t A351196 Array[DivisorSum[#, #^8 &, PrimeQ] &, 50]
%t A351196 f[p_, e_] := p^8; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 20 2022 *)
%o A351196 (Python)
%o A351196 from sympy import primefactors
%o A351196 def A351196(n): return sum(p**8 for p in primefactors(n)) # _Chai Wah Wu_, Feb 05 2022
%Y A351196 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).
%Y A351196 Cf. A010051.
%K A351196 nonn
%O A351196 1,2
%A A351196 _Wesley Ivan Hurt_, Feb 04 2022