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

1,2

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

Links

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

Example

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

Prog

(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

Crossrefs

Subsequence of A238985.

Sequence in context: A134810 A173689 A004871 * A191872 A280355 A001104

Adjacent sequences: A059402 A059403 A059404 * A059406 A059407 A059408

Keyword

base,nice,nonn

Author

Erich Friedman, Jan 29 2001

Extensions

More terms from Erich Friedman, Apr 01 2003

Offset changed by Reinhard Zumkeller, Apr 29 2015

Status

approved