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A351246 a(n) = n^6 * Sum_{p|n, p prime} 1/p^6.

%I A351246 #19 Jul 15 2025 22:42:43
%S A351246 0,1,1,64,1,793,1,4096,729,15689,1,50752,1,117713,16354,262144,1,
%T A351246 578097,1,1004096,118378,1771625,1,3248128,15625,4826873,531441,
%U A351246 7533632,1,12437281,1,16777216,1772290,24137633,133274,36998208,1,47045945,4827538,64262144,1,93342313
%N A351246 a(n) = n^6 * Sum_{p|n, p prime} 1/p^6.
%C A351246 Dirichlet convolution of A010051(n) and n^6. - _Wesley Ivan Hurt_, Jul 15 2025
%H A351246 Seiichi Manyama, <a href="/A351246/b351246.txt">Table of n, a(n) for n = 1..10000</a>
%F A351246 a(A000040(n)) = 1.
%F A351246 a(n) = Sum_{d|n} A069091(d)*A001221(n/d). - _Ridouane Oudra_, Jul 14 2025
%F A351246 From _Wesley Ivan Hurt_, Jul 15 2025: (Start)
%F A351246 a(n) = Sum_{d|n} c(d) * (n/d)^6, where c = A010051.
%F A351246 a(p^k) = p^(6*k-6) for p prime and k>=1. (End)
%e A351246 a(6) = 793; a(6) = 6^6 * Sum_{p|6, p prime} 1/p^6 = 46656 * (1/2^6 + 1/3^6) = 793.
%t A351246 Array[#^6*DivisorSum[#, 1/#^6 &, PrimeQ] &, 50] (* _Wesley Ivan Hurt_, Jul 15 2025 *)
%Y A351246 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), this sequence (k=6), A351247 (k=7), A351248 (k=8), A351249 (k=9), A351262 (k=10).
%Y A351246 Cf. A000040, A001221, A010051, A069091.
%K A351246 nonn
%O A351246 1,4
%A A351246 _Wesley Ivan Hurt_, Feb 05 2022