%I #19 Jun 22 2024 18:35:11

%S 0,128,2187,128,78125,2315,823543,128,2187,78253,19487171,2315,

%T 62748517,823671,80312,128,410338673,2315,893871739,78253,825730,

%U 19487299,3404825447,2315,78125,62748645,2187,823671,17249876309,80440,27512614111,128,19489358,410338801

%N Sum of the 7th powers of the primes dividing n.

%C Inverse Möbius transform of n^7 * c(n), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 22 2024

%H Seiichi Manyama, <a href="/A351195/b351195.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{p|n, p prime} p^7.

%F G.f.: Sum_{k>=1} prime(k)^7 * x^prime(k) / (1 - x^prime(k)). - _Ilya Gutkovskiy_, Feb 16 2022

%F Additive with a(p^e) = p^7. - _Amiram Eldar_, Jun 20 2022

%F a(n) = Sum_{d|n} d^7 * c(d), where c = A010051. - _Wesley Ivan Hurt_, Jun 22 2024

%t Array[DivisorSum[#, #^7 &, PrimeQ] &, 50]

%t f[p_, e_] := p^7; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jun 20 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), this sequence (k=7), A351196 (k=8), A351197 (k=9), A351198 (k=10).

%Y Cf. A010051.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Feb 04 2022