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A351247 a(n) = n^7 * Sum_{p|n, p prime} 1/p^7.

%I A351247 #19 Jul 15 2025 22:41:20
%S A351247 0,1,1,128,1,2315,1,16384,2187,78253,1,296320,1,823671,80312,2097152,
%T A351247 1,5062905,1,10016384,825730,19487299,1,37928960,78125,62748645,
%U A351247 4782969,105429888,1,181139311,1,268435456,19489358,410338801,901668,648051840,1,893871867,62750704
%N A351247 a(n) = n^7 * Sum_{p|n, p prime} 1/p^7.
%C A351247 Dirichlet convolution of A010051(n) and n^7. - _Wesley Ivan Hurt_, Jul 15 2025
%H A351247 Seiichi Manyama, <a href="/A351247/b351247.txt">Table of n, a(n) for n = 1..10000</a>
%F A351247 a(A000040(n)) = 1.
%F A351247 a(n) = Sum_{d|n} A069092(d)*A001221(n/d). - _Ridouane Oudra_, Jul 15 2025
%F A351247 From _Wesley Ivan Hurt_, Jul 15 2025: (Start)
%F A351247 a(n) = Sum_{d|n} c(d) * (n/d)^7, where c = A010051.
%F A351247 a(p^k) = p^(7*k-7) for p prime and k>=1. (End)
%e A351247 a(6) = 2315; a(6) = 6^7 * Sum_{p|6, p prime} 1/p^7 = 279936 * (1/2^7 + 1/3^7) = 2315.
%t A351247 Array[#^7*DivisorSum[#, 1/#^7 &, PrimeQ] &, 50] (* _Wesley Ivan Hurt_, Jul 15 2025 *)
%Y A351247 Sequences of the form n^k * Sum_{p|n, p prime} 1/p^k for k = 0..10: A001221 (k=0), A069359 (k=1), A322078 (k=2), A351242 (k=3), A351244 (k=4), A351245 (k=5), A351246 (k=6), this sequence (k=7), A351248 (k=8), A351249 (k=9), A351262 (k=10).
%Y A351247 Cf. A000040, A001221, A010051, A069092.
%K A351247 nonn
%O A351247 1,4
%A A351247 _Wesley Ivan Hurt_, Feb 05 2022