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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

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

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1296 = (1)(2^2)(9)(6^2)

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

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

(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

Offset changed bySubsequence of A238985.

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0,1,2

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

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_Erich Friedman (efriedma(AT)stetson.edu), _, Jan 29 2001

More terms from _Erich Friedman (efriedma(AT)stetson.edu), _, Apr 01 2003

Numbers which 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

0,2

1296 = (1)(2^2)(9)(6^2)

base,nice,nonn

Erich Friedman (efriedma(AT)stetson.edu), Jan 29 2001

More terms from Erich Friedman (efriedma(AT)stetson.edu), Apr 01 2003

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