cp's OEIS Frontend

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

%I A133809 #10 Apr 14 2015 11:40:38
%S A133809 1,2,4,8,16,18,32,54,64,108,128,162,256,324,486,512,648,972,1024,1458,
%T A133809 1944,2048,2250,2916,3888,4096,4374,5832,8192,8748,11250,11664,13122,
%U A133809 16384,17496,23328,26244,32768,33750,34992,39366,52488,56250,65536
%N A133809 Numbers that are primally tight, have 2 as first prime and strictly ascending powers.
%C A133809 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.
%C A133809 Subset of A073491, A133811 and A133808.
%H A133809 Reinhard Zumkeller, <a href="/A133809/b133809.txt">Table of n, a(n) for n = 1..10000</a>
%e A133809 36 = 2^2*3^2 with both exponents being equal is not in the sequence.
%o A133809 (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
%o A133809 (Haskell)
%o A133809 import Data.Set (singleton, deleteFindMin, insert)
%o A133809 a133809 n = a133809_list !! (n-1)
%o A133809 a133809_list = 1 : f (singleton (2, 2, 1)) where
%o A133809    f s = y : f (insert (y*p, p, e+1) $ insert (y*q^(e+1), q, e+1) s')
%o A133809              where q = a151800 p
%o A133809                    ((y, p, e), s') = deleteFindMin s
%o A133809 -- _Reinhard Zumkeller_, Apr 14 2015
%Y A133809 Cf. A025487, A087980, A073491, A133808-A133813.
%Y A133809 Cf. A027748, A124010, A151800, A000040, A145108 (subsequence).
%K A133809 nonn
%O A133809 1,2
%A A133809 _Olivier Gérard_, Sep 23 2007