%I #11 Feb 06 2022 02:09:26
%S 0,1,1,256,1,6817,1,65536,6561,390881,1,1745152,1,5765057,397186,
%T 16777216,1,44726337,1,100065536,5771362,214359137,1,446758912,390625,
%U 815730977,43046721,1475854592,1,2664570241,1,4294967296,214365442,6975757697,6155426,11449942272
%N a(n) = n^8 * Sum_{p|n, p prime} 1/p^8.
%F a(A000040(n)) = 1.
%e a(6) = 6817; a(6) = 6^8 * Sum_{p|6, p prime} 1/p^8 = 1679616 * (1/2^8 + 1/3^8) = 6817.
%o (Python)
%o from sympy import primefactors
%o def A351248(n): return sum((n//p)**8 for p in primefactors(n)) # _Chai Wah Wu_, Feb 05 2022
%Y 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), A351247 (k=7), this sequence (k=8), A351249 (k=9), A351262 (k=10).
%Y Cf. A000040.
%K nonn
%O 1,4
%A _Wesley Ivan Hurt_, Feb 05 2022