A133808 - OEIS

%I #10 Apr 14 2015 11:40:25

%S 1,2,4,6,8,16,18,30,32,36,54,64,108,128,150,162,210,216,256,324,450,

%T 486,512,648,750,900,972,1024,1296,1458,1470,1944,2048,2250,2310,2916,

%U 3750,3888,4096,4374,4500,5832,6750,7350,7776,8192,8748,10290,11250

%N Numbers that are primally tight, have 2 as first prime and weakly ascending powers.

%C 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 Subset of A073491, A133810.

%H Reinhard Zumkeller, <a href="/A133808/b133808.txt">Table of n, a(n) for n = 1..10000</a>

%e 10 = 2*5 with missing prime factor 3 between 2 and 5 is not in the sequence.

%e 12 = 2^2*3 with 2's exponent > 3's exponent is not in the sequence.

%o (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 (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a133808 n = a133808_list !! (n-1)

%o a133808_list = 1 : f (singleton (2, 2, 1)) where

%o    f s = y : f (insert (y * p, p, e + 1) $ insert (y * q^e, q, e) s')

%o              where q = a151800 p

%o                    ((y, p, e), s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Apr 13 2015

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

%Y Cf. A027748, A124010, A151800, A000040.

%K nonn

%O 1,2

%A _Olivier Gérard_, Sep 23 2007