%I #10 Jan 10 2020 09:18:46

%S 1,2,3,4,5,6,7,8,9,128,135,175,384,432,672,735,1296,1715,6144,6912,

%T 13824,18432,23328,34992,82944,93312,131712,248832,442368,1492992,

%U 2239488,2333772,2612736,3981312,4128768,4741632,9289728,12192768

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

%C 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

%H Reinhard Zumkeller, <a href="/A059405/b059405.txt">Table of n, a(n) for n = 1..120</a>

%e a(17) = 1296 = (1)(2^2)(9)(6^2);

%e a(32) = 2333772 = (2)(3)(3)(3^3)(7)(7^3)(2).

%o (Haskell)

%o a059405 n = a059405_list !! (n-1)

%o a059405_list = filter f a238985_list where

%o f x = all (== 0) (map (mod x) digs) && g x digs where

%o g z [] = z == 1

%o g z ds'@(d:ds) = r == 0 && (h z' ds' || g z' ds)

%o where (z', r) = divMod z d

%o h z [] = z == 1

%o h z ds'@(d:ds) = r == 0 && h z' ds' || g z ds

%o where (z', r) = divMod z d

%o digs = map (read . return) $ filter (/= '1') $ show x

%o -- _Reinhard Zumkeller_, Apr 29 2015

%Y Subsequence of A238985.

%K base,nice,nonn

%O 1,2

%A _Erich Friedman_, Jan 29 2001

%E More terms from _Erich Friedman_, Apr 01 2003

%E Offset changed by _Reinhard Zumkeller_, Apr 29 2015