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

Author

Vladimir Shevelev, Sep 24 2014

Keywords

• nonn

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

• Vladimir Shevelev , A classification of the positive integers over primes

Crossrefs

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

Extensions

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