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Sum of 4th powers of distinct prime divisors of n that are <= sqrt(n).
1

%I #5 Aug 20 2021 22:52:43

%S 0,0,0,16,0,16,0,16,81,16,0,97,0,16,81,16,0,97,0,16,81,16,0,97,625,16,

%T 81,16,0,722,0,16,81,16,625,97,0,16,81,641,0,97,0,16,706,16,0,97,2401,

%U 641,81,16,0,97,625,2417,81,16,0,722,0,16,2482,16,625,97,0,16,81,3042

%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)^2) / (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]^2)/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A001159, A005065, A005068, A063962, A097974, A098002, A347143, A347158, A347159.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Aug 20 2021