A050480 Numbers that can be written as a concatenation of distinct proper divisors.

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

Offset

1,1

Comments

The number of terms less than 10^k: 0, 5, 64, 395, 2406, 13417, 78268, ..., . - Robert G. Wilson v, Apr 04 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

132 is divisible by 1, 3 & 2.

Mathematica

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 *)

Prog

(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
-- Reinhard Zumkeller, Apr 04 2011

Crossrefs

Cf. A032742.

Sequence in context: A342758 A274550 A253235 * A290508 A063604 A357867

Adjacent sequences: A050477 A050478 A050479 * A050481 A050482 A050483

Keyword

base,easy,nice,nonn

Author

Erich Friedman, Dec 24 1999

Extensions

Offset adjusted by Reinhard Zumkeller, Apr 04 2011

Status

approved