A073646 Least number formed by concatenating the prime factors of n in base 10.

1, 2, 3, 22, 5, 23, 7, 222, 33, 25, 11, 223, 13, 27, 35, 2222, 17, 233, 19, 225, 37, 112, 23, 2223, 55, 132, 333, 227, 29, 235, 31, 22222, 113, 172, 57, 2233, 37, 192, 133, 2225, 41, 237, 43, 1122, 335, 223, 47, 22223, 77, 255, 173, 1322, 53, 2333, 115, 2227

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2002

Keywords

• nonn
• base
• look

Comments

a(n)<=A037276(n) for all n and a(n)=A037276(n) for n<22, a(22) = a(2*11) = 112 <> A037276(22) = 211.

Examples

			a(6) = a(2*3) = 23 < 32; a(66) = a(2*3*11) = 1123 < 1132 < 2113 < 2311 < 3112 < 3211.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Different from A037276. Cf. A084797.

Programs

Haskell

import Data.List (sort)
a073646 :: Integer -> Integer
a073646 = read . concat . sort . map show . a027746_row
-- Reinhard Zumkeller, Jul 13 2013

Mathematica

con[n_, k_] := Nest[Join[{#}, {n}] &, n, k - 1]; Table[Min[FromDigits /@ Flatten /@ IntegerDigits[Permutations[Flatten[con @@@ FactorInteger[n]]]]], {n, 56}] (* Jayanta Basu, Jul 04 2013 *)

Formula

Sort {A027746(n,k): k=1..A001222(n)} lexicographically and concatenate. - Reinhard Zumkeller, Jul 13 2013