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%I #5 Aug 20 2021 22:52:24
%S 0,0,0,0,0,8,0,8,0,8,0,35,0,8,27,8,0,35,0,8,27,8,0,35,0,8,27,8,0,160,
%T 0,8,27,8,125,35,0,8,27,133,0,35,0,8,152,8,0,35,0,133,27,8,0,35,125,
%U 351,27,8,0,160,0,8,370,8,125,35,0,8,27,476,0,35,0,8,152
%N Sum of cubes of distinct prime divisors of n that are < sqrt(n).
%F G.f.: Sum_{k>=1} prime(k)^3 * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).
%t Table[DivisorSum[n, #^3 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 75}]
%t nmax = 75; CoefficientList[Series[Sum[Prime[k]^3 x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y Cf. A001158, A005064, A005067, A333806, A333808, A339354, A347156, A347158.
%K nonn
%O 1,6
%A _Ilya Gutkovskiy_, Aug 20 2021
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