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A333808
Sum of distinct prime divisors of n that are < sqrt(n).
5
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, 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, 2, 3, 14, 0, 5, 0, 2, 8, 2, 7, 5, 0, 7, 3, 2, 0, 12, 5, 2, 3, 2, 0, 10
OFFSET
1,6
FORMULA
G.f.: Sum_{k>=1} prime(k) * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).
MATHEMATICA
Table[DivisorSum[n, # &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 90}]
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 05 2020
STATUS
approved