A059405 Numbers that are the product of their digits raised to positive integer powers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 128, 135, 175, 384, 432, 672, 735, 1296, 1715, 6144, 6912, 13824, 18432, 23328, 34992, 82944, 93312, 131712, 248832, 442368, 1492992, 2239488, 2333772, 2612736, 3981312, 4128768, 4741632, 9289728, 12192768

Offset: 1

Author

Erich Friedman, Jan 29 2001

Keywords

• base
• nice
• nonn

Comments

The second example suggests that a repeated digit must divide the number at least as many times as it occurs, i.e., "distinct [digits]" in the definition would give a different (super)set. What would be the additional terms? - M. F. Hasler, Jan 05 2020

Examples

			a(17) = 1296 = (1)(2^2)(9)(6^2);
a(32) = 2333772 = (2)(3)(3)(3^3)(7)(7^3)(2).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..120

Crossrefs

Subsequence of A238985.

Programs

Haskell

a059405 n = a059405_list !! (n-1)
a059405_list = filter f a238985_list where
   f x = all (== 0) (map (mod x) digs) && g x digs where
         g z []         = z == 1
         g z ds'@(d:ds) = r == 0 && (h z' ds' || g z' ds)
                          where (z', r) = divMod z d
         h z []         = z == 1
         h z ds'@(d:ds) = r == 0 && h z' ds' || g z ds
                          where (z', r) = divMod z d
         digs = map (read . return) $ filter (/= '1') $ show x
-- Reinhard Zumkeller, Apr 29 2015

Extensions

More terms from Erich Friedman, Apr 01 2003

Offset changed by Reinhard Zumkeller, Apr 29 2015