

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
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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[4000], 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: A163750 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



