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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
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).
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: A356660 A167153 A298298 * A055983 A318700 A180157
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