The On-Line Encyclopedia of Integer Sequences (OEIS)

A247393 revision #34

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

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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