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A247834 Maximal non-semiprime number which is a "preprime" of the n-th kind (defined in comment in A247395). 3
8, 45, 125, 343, 325, 833, 1331, 1573, 2197, 2057, 3211, 3289, 4913, 4901, 6859, 6647, 8303, 10051, 10469, 11191, 12167, 15341, 16399, 17081, 18259, 22103, 24389, 26071, 29791, 27347, 31117, 35557, 36163, 36859, 39401, 42439, 50653, 50933, 52111, 56129, 56699 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: the sequence contains all cubes of primes, except for 3^3 (cf. A030078).

Prime(n)^3 is in the sequence iff the interval [prime(n)^(3/2), prime(n)*sqrt(prime(n+1))] contains a prime.

A simple algorithm for finding the position k=k(n) for which a(k) = prime(n)^3 is given in A247835 (see formula and example there).

Conjecture: every term has the form a(n)= p*q*r, where p<=q<=r are primes.

LINKS

Table of n, a(n) for n=1..41.

Vladimir Shevelev , A classification of the positive integers over primes

CROSSREFS

Cf. A030078, A156759, A247393, A247394, A247395, A247396, A247509, A247510, A247511, A247606, A247835, A247867.

Sequence in context: A075863 A118838 A153828 * A210378 A247534 A100648

Adjacent sequences:  A247831 A247832 A247833 * A247835 A247836 A247837

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Sep 24 2014

EXTENSIONS

More terms from Peter J. C. Moses, Sep 24 2014

STATUS

approved

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Last modified November 15 05:50 EST 2019. Contains 329144 sequences. (Running on oeis4.)