A226272 Distinct numbers that can be written as u^v, where u and v are not necessarily distinct digits of n in decimal representation, table read by rows.

1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 0, 1, 1, 1, 2, 4, 1, 3, 27, 1, 4, 256, 1, 5, 3125, 1, 6, 46656, 1, 7, 823543, 1, 8, 16777216, 1, 9, 387420489, 0, 1, 4, 1, 2, 4, 4, 4, 8, 9, 27, 4, 16, 256, 4, 25, 32, 3125, 4, 36, 64, 46656

Offset: 0

Author

Reinhard Zumkeller, Jul 09 2013

Keywords

• nonn
• base
• tabf

Comments

Row lengths: A226273;

T(n,k) <= 9^9 = 387420489;

largest term of n-th row = A054055(n)^A054055(n);

row(n) is contained in row(10*n+d), 0 <= d <= 9;

see A226277 for numbers m such that m is contained in m-th row.

Examples

			.   n          row(n)                                    A226273(n)
. ---   ---------------------   -----------------------  ----------
.   0   [1]                     {0^0}                          1
.   1   [1]                     {1^1}                          1
.   2   [4]                     {2^2}                          1
.   3   [27]                    {3^3}                          1
.   4   [256]                   {4^4}                          1
.   5   [3125]                  {5^5}                          1
.   6   [46656]                 {6^6}                          1
.   7   [823543]                {7^7}                          1
.   8   [16777216]              {8^8}                          1
.   9   [387420489]             {9^9}                          1
.  10   [0,1]                   {0^1, 0^0=1^0=1^1}             2
.  11   [1]  = row(1)           {1^1}                          1
.  12   [1,2,4]                 {1^1=1^2, 2^1, 2^2}            3
.  13   [1,3,27]                {1^1=1^3, 3^1, 3^3}            3
.  14   [1,4,256]               {1^1=1^4, 4^1, 4^4}            3
.  15   [1,5,3125]              {1^1=1^5, 5^1, 5^5}            3
.  16   [1,6,46656]             {1^1=1^6, 6^1, 6^6}            3
.  17   [1,7,823543]            {1^1=1^7, 7^1, 7^7}            3
.  18   [1,8,16777216]          {1^1=1^8, 8^1, 8^8}            3
.  19   [1,9,387420489]         {1^1=1^9, 9^1, 9^9}            3
.  20   [0,1,4]                 {0^2, 0^0=2^0, 2^2}            3
.  21   [1,2,4]  = row(12)      {1^1=1^2, 2^1, 2^2}            3
.  22   [4]  = row(2)           {2^2}                          1
.  23   [4,8,9,27]              {2^2, 2^3, 3^2, 3^3}           4
.  24   [4,16,256]              {2^2, 2^4=4^2, 4^4}            3
.  25   [4,25,32,3125]          {2^2, 5^2, 2^5, 5^5}           4
.  26   [4,36,64,46656]         {2^2, 6^6, 2^6, 6^6}           4
.  27   [4,49,128,823543]       {2^2, 7^2, 2^7, 7^7}           4
.  28   [4,64,256,16777216]     {2^2, 8^2, 2^8, 8^8}           4
.  29   [4,81,512,387420489]    {2^2, 9^2, 2^9, 9^9}           4
.  30   [0,1,27]                {0^3, 0^0=3^0, 3^3}            3 .
		

Links

• Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened

Crossrefs

Cf. A000312.

Programs

Haskell

import Data.List (nub, sort)
a226272 n k = a226272_tabf !! n !! k
a226272_row n = sort $ nub [u ^ v | u <- digs, v <- digs]
                where digs = nub $ map (read . return) $ show n
a226272_tabf = map a226272_row [0..]