A247393 Numbers n such that the second maximal prime <= sqrt(n) is the least prime divisor of n.

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

Offset: 1

Author

Vladimir Shevelev, Sep 16 2014

Keywords

• nonn

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).

Examples

			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).
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
• Vladimir Shevelev, A classification of the positive integers over primes

Crossrefs

Cf. A156759.

Programs

Mathematica

Select[Range[4000], Prime[PrimePi[Sqrt[#]]-1] == FactorInteger[#][[1,1]] &] (* Indranil Ghosh, Mar 08 2017 *)

PARI

select(n->prime(primepi(sqrtint(n))-1)==factor(n)[1, 1], vector(10^4, x, x+8)) \\ Jens Kruse Andersen, Sep 17 2014

Formula

lpf(a(n)) = prime(pi(sqrt(a(n)))-1), where pi(n) = A000720(n).

Extensions

More terms from Peter J. C. Moses, Sep 16 2014

a(52..10000) from Jens Kruse Andersen, Sep 17 2014