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

1,2

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.

Links

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

Example

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.

Prog

(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
(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

Crossrefs

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

Cf. A027748, A124010, A151800, A000040.

Sequence in context: A258119 A073696 A058602 * A160560 A332291 A093109

Adjacent sequences: A133805 A133806 A133807 * A133809 A133810 A133811

Keyword

nonn

Author

Olivier Gérard, Sep 23 2007

Status

approved