A050480 - OEIS

%I #16 Feb 12 2014 18:16:06

%S 12,15,24,36,48,110,120,124,125,126,128,132,135,150,162,168,175,184,

%T 210,216,220,240,248,250,264,312,315,324,330,360,375,384,396,412,416,

%U 420,432,440,480,510,520,525,550,612,624,630,648,660,672,714,728,735

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

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

%H Reinhard Zumkeller, <a href="/A050480/b050480.txt">Table of n, a(n) for n = 1..1000</a>

%e 132 is divisible by 1, 3 & 2.

%t 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 *)

%o (Haskell)

%o import Data.List (permutations, subsequences, isInfixOf)

%o a050480 n = a050480_list !! (n-1)

%o a050480_list = filter chi [2..] where

%o    chi x = xs `elem` (map concat $ choices divs) where

%o       choices = concat . (map permutations) . subsequences

%o       divs = filter (`isInfixOf` xs)

%o                     $ map show $ filter ((== 0) . mod x) [1..a032742 x]

%o       xs = show x

%o -- _Reinhard Zumkeller_, Apr 04 2011

%Y Cf. A032742.

%K base,easy,nice,nonn

%O 1,1

%A _Erich Friedman_, Dec 24 1999

%E Offset adjusted by _Reinhard Zumkeller_, Apr 04 2011