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
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..]
Comments