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A059405 Numbers that are the product of their digits raised to positive integer powers. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 02:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)