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Sum of distinct prime divisors of n that are < sqrt(n).
5

%I #4 Apr 05 2020 23:28:11

%S 0,0,0,0,0,2,0,2,0,2,0,5,0,2,3,2,0,5,0,2,3,2,0,5,0,2,3,2,0,10,0,2,3,2,

%T 5,5,0,2,3,7,0,5,0,2,8,2,0,5,0,7,3,2,0,5,5,9,3,2,0,10,0,2,10,2,5,5,0,

%U 2,3,14,0,5,0,2,8,2,7,5,0,7,3,2,0,12,5,2,3,2,0,10

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

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

%t Table[DivisorSum[n, # &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 90}]

%t nmax = 90; CoefficientList[Series[Sum[Prime[k] x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A008472, A070039, A097974, A333806, A333807.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Apr 05 2020