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A247393
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Numbers n such that the second maximal prime <= sqrt(n) is the least prime divisor of n.
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11
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10, 12, 14, 16, 18, 20, 22, 24, 27, 33, 39, 45, 55, 65, 85, 95, 115, 133, 161, 187, 209, 253, 299, 391, 493, 527, 551, 589, 703, 779, 817, 851, 943, 1073, 1189, 1247, 1363, 1457, 1643, 1739, 1927, 2173, 2279, 2537, 2623, 2867, 3149, 3337, 3431, 3551, 3953
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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 second kind in contrast to A156759 for n>=2, for which the maximal prime <= sqrt(n) is the least prime divisor of n. Terms of A156759 (n>=2) we call "preprimes" (cf. comment there).
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LINKS
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FORMULA
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lpf(a(n)) = prime(pi(sqrt(a(n))-1), where pi(n) = A000720(n).
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EXAMPLE
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a(1)=10. Indeed, in interval [2,sqrt(10)] we have two primes: 2 and 3. Maximal from them 3, the second maximal is 2, and 2=lpf(10).
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MATHEMATICA
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Select[Range[4000], Prime[PrimePi[Sqrt[#]]-1] == FactorInteger[#][[1, 1]] &] (* Indranil Ghosh, Mar 08 2017 *)
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PROG
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(PARI) select(n->prime(primepi(sqrtint(n))-1)==factor(n)[1, 1], vector(10^4, x, x+8)) \\ 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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