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 A247393 Numbers n such that the second maximal prime <= sqrt(n) is the least prime divisor of n. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). LINKS Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 Vladimir Shevelev, A classification of the positive integers over primes FORMULA lpf(a(n)) = prime(pi(sqrt(a(n))-1), where pi(n) = A000720(n). EXAMPLE 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). MATHEMATICA Select[Range, Prime[PrimePi[Sqrt[#]]-1] == FactorInteger[#][[1, 1]] &] (* Indranil Ghosh, Mar 08 2017 *) PROG (PARI) select(n->prime(primepi(sqrtint(n))-1)==factor(n)[1, 1], vector(10^4, x, x+8)) \\ Jens Kruse Andersen, Sep 17 2014 CROSSREFS Cf. A156759. Sequence in context: A356660 A167153 A298298 * A055983 A318700 A180157 Adjacent sequences: A247390 A247391 A247392 * A247394 A247395 A247396 KEYWORD nonn AUTHOR Vladimir Shevelev, Sep 16 2014 EXTENSIONS More terms from Peter J. C. Moses, Sep 16 2014 a(52..10000) from Jens Kruse Andersen, Sep 17 2014 STATUS approved

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Last modified February 7 07:00 EST 2023. Contains 360112 sequences. (Running on oeis4.)