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A050480
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Numbers that can be written as a concatenation of distinct proper divisors.
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1
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12, 15, 24, 36, 48, 110, 120, 124, 125, 126, 128, 132, 135, 150, 162, 168, 175, 184, 210, 216, 220, 240, 248, 250, 264, 312, 315, 324, 330, 360, 375, 384, 396, 412, 416, 420, 432, 440, 480, 510, 520, 525, 550, 612, 624, 630, 648, 660, 672, 714, 728, 735
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The number of terms less than 10^k: 0, 5, 64, 395, 2406, 13417, 78268, ..., . - Robert G. Wilson v, Apr 04 2011
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LINKS
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EXAMPLE
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132 is divisible by 1, 3 & 2.
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MATHEMATICA
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f[x_, y_] := (y == Take[x, Min[Length@ y, Length@ x]]); g[{}, _] := True; g[LL_, DD_] := Module[{a = Select[DD, f[LL, IntegerDigits@ #] &]}, Or @@ Map[ g[ Drop[ LL, Length@ IntegerDigits@ #], Complement[DD, {#}]] &, a]]; fQ[n_] := g[IntegerDigits@ n, Most@ Divisors@ n]; Select[ Range@ 2000, fQ] (* Robert G. Wilson v, Apr 04 2011 *)
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PROG
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(Haskell)
import Data.List (permutations, subsequences, isInfixOf)
a050480 n = a050480_list !! (n-1)
a050480_list = filter chi [2..] where
chi x = xs `elem` (map concat $ choices divs) where
choices = concat . (map permutations) . subsequences
divs = filter (`isInfixOf` xs)
$ map show $ filter ((== 0) . mod x) [1..a032742 x]
xs = show x
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CROSSREFS
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KEYWORD
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base,easy,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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