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A052202
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Numbers k such that the product of the logarithms of k's prime factors is greater than their sum.
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1
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77, 85, 91, 95, 115, 119, 121, 133, 143, 145, 155, 161, 169, 185, 187, 203, 205, 209, 215, 217, 221, 235, 245, 247, 253, 259, 265, 275, 287, 289, 295, 299, 301, 305, 319, 323, 325, 329, 335, 341, 343, 355, 357, 361, 363, 365, 371, 377, 385, 391, 395, 399
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OFFSET
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1,1
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COMMENTS
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First even term is 1334.
Previous name was: If p^a(p,n) is highest power of p that divides n, then Product_(p=primes) [log(p)^a(p,n) ] > log(n).
Primes are counted with multiplicity.
Does this sequence have asymptotic density 1?
a(100000) = 189835. (End)
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LINKS
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EXAMPLE
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245 is included because 245 = 5*7^2 and log(5)*log(7)^2 > log(245).
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MATHEMATICA
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aQ[n_] := Times@@Power@@@({Log[#1], #2} & @@@FactorInteger[n]) > Log[n]; Select[Range[400], aQ] (* Amiram Eldar, Dec 03 2018 *)
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PROG
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(PARI) isok(n) = my(f=factor(n)); prod(k=1, #f~, log(f[k, 1])^f[k, 2]) > log(n); \\ Michel Marcus, Dec 04 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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