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A059405
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Numbers that are the product of their digits raised to positive integer powers.
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5
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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)
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OFFSET
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1,2
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COMMENTS
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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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LINKS
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EXAMPLE
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a(17) = 1296 = (1)(2^2)(9)(6^2);
a(32) = 2333772 = (2)(3)(3)(3^3)(7)(7^3)(2).
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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