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

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, 47, 48, 49, 53, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 96, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 135, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 175

Offset: 1

Author

Olivier Gérard, Sep 23 2007

Keywords

• nonn

Comments

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.

Subset of A073491, A133812.

Differs from A085233 starting n=22.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025487, A087980, A073491, A133808-A133812.

Cf. A027748, A124010, A049084, A020639, A000040, A087980.

Programs

Haskell

import Data.List (isPrefixOf)
a133813 n = a133813_list !! (n-1)
a133813_list = 1 : filter f [2..] where
   f x = isPrefixOf ps (dropWhile (< a020639 x) a000040_list) &&
           all (< 0) (zipWith (-) (tail es) es)
         where ps = a027748_row x; es = a124010_row x
-- Reinhard Zumkeller, Apr 14 2015

Formula

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