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A133809
Numbers that are primally tight, have 2 as first prime and strictly ascending powers.
4
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
1,2
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
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
KEYWORD
nonn
AUTHOR
Olivier Gérard, Sep 23 2007
STATUS
approved