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A347158
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Sum of 4th powers of distinct prime divisors of n that are < sqrt(n).
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3
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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, 16, 0, 722, 0, 16, 81, 16, 625, 97, 0, 16, 81, 641, 0, 97, 0, 16, 706, 16, 0, 97, 0, 641, 81, 16, 0, 97, 625, 2417, 81, 16, 0, 722, 0, 16, 2482, 16, 625, 97, 0, 16, 81, 3042
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OFFSET
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1,6
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} prime(k)^4 * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).
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MATHEMATICA
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Table[DivisorSum[n, #^4 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 70}]
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
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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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