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A133809 Numbers that are primally tight, have 2 as first prime and strictly ascending powers. 3
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 (list; graph; refs; listen; history; text; internal format)
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, A133811 and A133808.

LINKS

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

EXAMPLE

36 = 2^2*3^2 with both exponents being equal 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)

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

CROSSREFS

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

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

Sequence in context: A088827 A316900 A076057 * A128700 A331579 A333225

Adjacent sequences:  A133806 A133807 A133808 * A133810 A133811 A133812

KEYWORD

nonn

AUTHOR

Olivier Gérard, Sep 23 2007

STATUS

approved

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Last modified April 18 05:44 EDT 2021. Contains 343072 sequences. (Running on oeis4.)