A133811 - OEIS

%I #12 Jun 04 2014 15:16:07

%S 1,2,3,4,5,7,8,9,11,13,16,17,18,19,23,25,27,29,31,32,37,41,43,47,49,

%T 53,54,59,61,64,67,71,73,75,79,81,83,89,97,101,103,107,108,109,113,

%U 121,125,127,128,131,137,139,149,151,157,162,163,167,169,173,179,181,191

%N Numbers that are primally tight and have strictly ascending powers.

%C All numbers of the form p_1^k1*p_2^k2*...*p_n^k_n, where k1 < k2 < ... < k_n and the p_i are n successive primes.

%C Subset of A073491, A133810.

%C Different from A082377 starting n=16.

%C Different from A000961 (prime powers) starting n=13.

%H Reinhard Zumkeller, <a href="/A133811/b133811.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o a133811 n = a133811_list !! (n-1)

%o a133811_list = 1 : filter f [2..] where

%o    f x = (and $ zipWith (<) eps $ tail eps) &&

%o          (all (== 1) $ zipWith (-) (tail ips) ips)

%o      where ips = map a049084 $ a027748_row x

%o            eps = a124010_row x

%o -- _Reinhard Zumkeller_, Nov 07 2012

%o (PARI) isok(n) = {my(f = factor(n)); my(nbf = #f~); my(lastp = 0); for (i=1, nbf, if (lastp && (f[i, 1] != nextprime(lastp+1)), return (0)); lastp = f[i, 1];); for (j=2, nbf, if (f[j,2] <= f[j-1,2], return (0));); return (1);} \\ _Michel Marcus_, Jun 04 2014

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

%Y Cf. A124010, A027748, A049084.

%K nonn

%O 1,2

%A _Olivier Gérard_, Sep 23 2007