A133808 Numbers that are primally tight, have 2 as first prime and weakly ascending powers.

1, 2, 4, 6, 8, 16, 18, 30, 32, 36, 54, 64, 108, 128, 150, 162, 210, 216, 256, 324, 450, 486, 512, 648, 750, 900, 972, 1024, 1296, 1458, 1470, 1944, 2048, 2250, 2310, 2916, 3750, 3888, 4096, 4374, 4500, 5832, 6750, 7350, 7776, 8192, 8748, 10290, 11250

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, A133810.

Examples

			10 = 2*5 with missing prime factor 3 between 2 and 5 is not in the sequence.
12 = 2^2*3 with 2's exponent > 3's exponent is not in the sequence.
		

Links

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

Crossrefs

Cf. A025487, A087980, A073491, A133809-A133813.

Cf. A027748, A124010, A151800, A000040.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a133808 n = a133808_list !! (n-1)
a133808_list = 1 : f (singleton (2, 2, 1)) where
   f s = y : f (insert (y * p, p, e + 1) $ insert (y * q^e, q, e) s')
             where q = a151800 p
                   ((y, p, e), s') = deleteFindMin s
-- Reinhard Zumkeller, Apr 13 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