A247834 - OEIS

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

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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