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A133811 Numbers that are primally tight and have strictly ascending powers.

%I A133811 #12 Jun 04 2014 15:16:07
%S A133811 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 A133811 53,54,59,61,64,67,71,73,75,79,81,83,89,97,101,103,107,108,109,113,
%U A133811 121,125,127,128,131,137,139,149,151,157,162,163,167,169,173,179,181,191
%N A133811 Numbers that are primally tight and have strictly ascending powers.
%C A133811 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 A133811 Subset of A073491, A133810.
%C A133811 Different from A082377 starting n=16.
%C A133811 Different from A000961 (prime powers) starting n=13.
%H A133811 Reinhard Zumkeller, <a href="/A133811/b133811.txt">Table of n, a(n) for n = 1..10000</a>
%o A133811 (Haskell)
%o A133811 a133811 n = a133811_list !! (n-1)
%o A133811 a133811_list = 1 : filter f [2..] where
%o A133811    f x = (and $ zipWith (<) eps $ tail eps) &&
%o A133811          (all (== 1) $ zipWith (-) (tail ips) ips)
%o A133811      where ips = map a049084 $ a027748_row x
%o A133811            eps = a124010_row x
%o A133811 -- _Reinhard Zumkeller_, Nov 07 2012
%o A133811 (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 A133811 Cf. A025487, A087980, A073491, A133808-A133813.
%Y A133811 Cf. A124010, A027748, A049084.
%K A133811 nonn
%O A133811 1,2
%A A133811 _Olivier Gérard_, Sep 23 2007