A133809 Numbers that are primally tight, have 2 as first prime and strictly ascending powers.

1, 2, 4, 8, 16, 18, 32, 54, 64, 108, 128, 162, 256, 324, 486, 512, 648, 972, 1024, 1458, 1944, 2048, 2250, 2916, 3888, 4096, 4374, 5832, 8192, 8748, 11250, 11664, 13122, 16384, 17496, 23328, 26244, 32768, 33750, 34992, 39366, 52488, 56250, 65536

Offset: 1

Author

Olivier Gérard, Sep 23 2007

Keywords

• nonn

Comments

All numbers of the form 2^k1*p_2^k2*...*p_n^k_n, where k1 < k2 < ... < k_n and the p_i are the n first primes.

Subset of A073491, A133811 and A133808.

Examples

			36 = 2^2*3^2 with both exponents being equal is not in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025487, A087980, A073491, A133808-A133813.

Cf. A027748, A124010, A151800, A000040, A145108 (subsequence).

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a133809 n = a133809_list !! (n-1)
a133809_list = 1 : f (singleton (2, 2, 1)) where
   f s = y : f (insert (y*p, p, e+1) $ insert (y*q^(e+1), q, e+1) s')
             where q = a151800 p
                   ((y, p, e), s') = deleteFindMin s
-- Reinhard Zumkeller, Apr 14 2015

PARI

isok(n) = {my(f = factor(n)); my(nbf = #f~); if (prod(i=1, nbf, prime(i)) ! = prod(i=1, nbf, f[i, 1]), return (0)); for (j=2, nbf, if (f[j,2] <= f[j-1,2], return (0));); return (1);} \\ Michel Marcus, Jun 04 2014