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 A351194 #19 Jun 22 2024 18:33:03
%S A351194 0,64,729,64,15625,793,117649,64,729,15689,1771561,793,4826809,117713,
%T A351194 16354,64,24137569,793,47045881,15689,118378,1771625,148035889,793,
%U A351194 15625,4826873,729,117713,594823321,16418,887503681,64,1772290,24137633,133274,793,2565726409
%N A351194 Sum of the 6th powers of the primes dividing n.
%C A351194 Inverse Möbius transform of n^6 * c(n), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 22 2024
%H A351194 Seiichi Manyama, <a href="/A351194/b351194.txt">Table of n, a(n) for n = 1..10000</a>
%F A351194 a(n) = Sum_{p|n, p prime} p^6.
%F A351194 G.f.: Sum_{k>=1} prime(k)^6 * x^prime(k) / (1 - x^prime(k)). - _Ilya Gutkovskiy_, Feb 16 2022
%F A351194 Additive with a(p^e) = p^6. - _Amiram Eldar_, Jun 20 2022
%F A351194 a(n) = Sum_{d|n} d^6 * c(d), where c = A010051. - _Wesley Ivan Hurt_, Jun 22 2024
%t A351194 Array[DivisorSum[#, #^6 &, PrimeQ] &, 50]
%t A351194 f[p_, e_] := p^6; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 20 2022 *)
%Y A351194 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), this sequence (k=6), A351195 (k=7), A351196 (k=8), A351197 (k=9), A351198 (k=10).
%Y A351194 Cf. A010051.
%K A351194 nonn
%O A351194 1,2
%A A351194 _Wesley Ivan Hurt_, Feb 04 2022