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Sum of 4th powers of distinct prime divisors of n that are < sqrt(n).
3

%I #4 Aug 20 2021 22:52:29

%S 0,0,0,0,0,16,0,16,0,16,0,97,0,16,81,16,0,97,0,16,81,16,0,97,0,16,81,

%T 16,0,722,0,16,81,16,625,97,0,16,81,641,0,97,0,16,706,16,0,97,0,641,

%U 81,16,0,97,625,2417,81,16,0,722,0,16,2482,16,625,97,0,16,81,3042

%N Sum of 4th powers of distinct prime divisors of n that are < sqrt(n).

%F G.f.: Sum_{k>=1} prime(k)^4 * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).

%t Table[DivisorSum[n, #^4 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 70}]

%t nmax = 70; CoefficientList[Series[Sum[Prime[k]^4 x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A001159, A005065, A005068, A333806, A333808, A347142, A347156, A347157.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Aug 20 2021