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A328260
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a(n) = n * omega(n).
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5
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0, 2, 3, 4, 5, 12, 7, 8, 9, 20, 11, 24, 13, 28, 30, 16, 17, 36, 19, 40, 42, 44, 23, 48, 25, 52, 27, 56, 29, 90, 31, 32, 66, 68, 70, 72, 37, 76, 78, 80, 41, 126, 43, 88, 90, 92, 47, 96, 49, 100, 102, 104, 53, 108, 110, 112, 114, 116, 59, 180, 61, 124, 126, 64, 130, 198, 67, 136, 138, 210
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} prime(k) * x^prime(k) / (1 - x^prime(k))^2.
a(n) = bigomega(rad(n)^n).
Define f(x) = #{n <= x: a(n) <= x}. Gabdullin & Iudelevich show that f(x) ~ x/log log x. - Charles R Greathouse IV, Mar 16 2022
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MATHEMATICA
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Table[n PrimeNu[n], {n, 1, 70}]
nmax = 70; CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 - x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(Magma) [0] cat [n*(#PrimeDivisors(n)):n in [2..70]]; // Marius A. Burtea, Oct 10 2019
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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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