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A347159
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Sum of cubes of distinct prime divisors of n that are <= sqrt(n).
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1
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0, 0, 0, 8, 0, 8, 0, 8, 27, 8, 0, 35, 0, 8, 27, 8, 0, 35, 0, 8, 27, 8, 0, 35, 125, 8, 27, 8, 0, 160, 0, 8, 27, 8, 125, 35, 0, 8, 27, 133, 0, 35, 0, 8, 152, 8, 0, 35, 343, 133, 27, 8, 0, 35, 125, 351, 27, 8, 0, 160, 0, 8, 370, 8, 125, 35, 0, 8, 27, 476, 0, 35, 0, 8, 152
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OFFSET
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1,4
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} prime(k)^3 * x^(prime(k)^2) / (1 - x^prime(k)).
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MATHEMATICA
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Table[DivisorSum[n, #^3 &, # <= Sqrt[n] && PrimeQ[#] &], {n, 1, 75}]
nmax = 75; CoefficientList[Series[Sum[Prime[k]^3 x^(Prime[k]^2)/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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