A247394 Numbers n for which the third maximal prime <= sqrt(n) is the least prime divisor of n.

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

Offset: 1

Author

Vladimir Shevelev, Sep 16 2014

Keywords

• nonn

Comments

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.

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, A247393.

Programs

Mathematica

Select[Range[4000], Prime[PrimePi[Sqrt[#]]-2] == FactorInteger[#][[1,1]] &] (* Indranil Ghosh, Mar 08 2017 *)

PARI

select(n->prime(primepi(sqrtint(n))-2)==factor(n)[1, 1], vector(10^4, x, x+24)) \\ Jens Kruse Andersen, Sep 17 2014

Formula

lpf(a(n)) = prime(pi(isqrt(a(n)))-2), with pi(n) = A000720(n), lpf(n) = A020639(n) and isqrt(n) = A000196(n).

Extensions

Terms up to a(54) from Peter J. C. Moses, Sep 16 2014