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

1,1

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A156759, A247393.

Sequence in context: A042400 A042401 A042402 * A056081 A081644 A256619

Adjacent sequences: A247391 A247392 A247393 * A247395 A247396 A247397

Keyword

nonn

Author

Vladimir Shevelev, Sep 16 2014

Extensions

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

Status

approved