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A133813 Numbers that are primally tight and have strictly descending powers.

%I A133813 #9 Jun 30 2025 16:52:38
%S A133813 1,2,3,4,5,7,8,9,11,12,13,16,17,19,23,24,25,27,29,31,32,37,41,43,45,
%T A133813 47,48,49,53,59,61,64,67,71,72,73,79,81,83,89,96,97,101,103,107,109,
%U A133813 113,121,125,127,128,131,135,137,139,144,149,151,157,163,167,169,173,175
%N A133813 Numbers that are primally tight and have strictly descending powers.
%C A133813 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 A133813 Subset of A073491, A133812.
%C A133813 Differs from A085233 starting n=22.
%H A133813 Reinhard Zumkeller, <a href="/A133813/b133813.txt">Table of n, a(n) for n = 1..10000</a>
%F A133813 A049084(A027748(a(n),k+1)) = A049084(A027748(a(n),k)) + 1 and A124010(a(n),k+1) < A124010(a(n),k), 1 <= k < A001221(a(n)). - _Reinhard Zumkeller_, Apr 14 2015
%o A133813 (Haskell)
%o A133813 import Data.List (isPrefixOf)
%o A133813 a133813 n = a133813_list !! (n-1)
%o A133813 a133813_list = 1 : filter f [2..] where
%o A133813    f x = isPrefixOf ps (dropWhile (< a020639 x) a000040_list) &&
%o A133813            all (< 0) (zipWith (-) (tail es) es)
%o A133813          where ps = a027748_row x; es = a124010_row x
%o A133813 -- _Reinhard Zumkeller_, Apr 14 2015
%Y A133813 Cf. A025487, A087980, A073491, A133808-A133812.
%Y A133813 Cf. A027748, A124010, A049084, A020639, A000040, A087980.
%K A133813 nonn
%O A133813 1,2
%A A133813 _Olivier Gérard_, Sep 23 2007