A247834 Maximal non-semiprime number which is a "preprime" of the n-th kind (defined in comment in A247395).

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

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