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A247394
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Numbers n for which the third maximal prime <= sqrt(n) is the least prime divisor of n.
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10
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26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 111, 117, 125, 145, 155, 203, 217, 259, 287, 319, 341, 377, 403, 481, 629, 697, 731, 799, 893, 989, 1081, 1219, 1357, 1537, 1829, 1961, 2183, 2419, 2501, 2747, 2881, 3053
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OFFSET
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1,1
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COMMENTS
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These numbers we call "preprimes" of the third kind in contrast to A156759 for n>=2, for which the maximal prime <= sqrt(n) is the least prime divisor of n; and to A247393 for which the second maximal prime <= sqrt(n) is the least prime divisor of n.
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LINKS
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FORMULA
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lpf(a(n)) = prime(pi(isqrt(a(n))-2), with pi(n) = A000720(n), lpf(n) = A020639(n) and isqrt(n) = A000196(n).
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MATHEMATICA
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Select[Range[4000], Prime[PrimePi[Sqrt[#]]-2] == FactorInteger[#][[1, 1]] &] (* Indranil Ghosh, Mar 08 2017 *)
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PROG
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(PARI) select(n->prime(primepi(sqrtint(n))-2)==factor(n)[1, 1], vector(10^4, x, x+24)) \\ Jens Kruse Andersen, Sep 17 2014
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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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