A145108 -id:A145108 - cp's OEIS frontend

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

Olivier Gérard, Sep 23 2007

nonn

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.

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

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

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

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

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

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

cp's OEIS Frontend

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

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