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A333750
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Number of prime power divisors of n that are <= sqrt(n).
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28
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0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1, 2, 0, 3, 0, 2, 1, 1, 1, 3, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 3, 1, 2, 1, 2, 0, 2, 1, 3, 1, 1, 0, 4, 0, 1, 2, 3, 1, 2, 0, 2, 1, 3, 0, 4, 0, 1, 2, 2, 1, 2, 0, 4, 2, 1, 0, 4, 1, 1, 1, 3, 0, 4, 1, 2, 1, 1, 1, 4, 0, 2, 2, 3
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OFFSET
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1,12
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LINKS
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FORMULA
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G.f.: Sum_{p prime, k>=1} x^(p^(2*k)) / (1 - x^(p^k)).
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MAPLE
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f:= proc(n) local p;
add(min(padic:-ordp(n, p), floor(1/2*log[p](n))), p=numtheory:-factorset(n))
end proc:
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MATHEMATICA
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Table[DivisorSum[n, 1 &, # <= Sqrt[n] && PrimePowerQ[#] &], {n, 1, 100}]
nmax = 100; CoefficientList[Series[Sum[Boole[PrimePowerQ[k]] x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(PARI) a(n) = sumdiv(n, d, (d^2<=n) && isprimepower(d)); \\ Michel Marcus, Apr 03 2020
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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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