A085079 Largest number with the prime signature of n using prime divisors of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 13, 14, 15, 16, 17, 18, 19, 50, 21, 22, 23, 54, 25, 26, 27, 98, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 250, 41, 42, 43, 242, 75, 46, 47, 162, 49, 50, 51, 338, 53, 54, 55, 686, 57, 58, 59, 150, 61, 62, 147, 64, 65, 66, 67, 578, 69, 70

Offset: 1

Author

Amarnath Murthy, Jul 01 2003

Keywords

• nonn

Comments

Though a large number of initial terms match, this sequence is different from A069799. Example: a(1500) = a(2^2*3*5^3) = 5^3*3^2*2 = 2250, whereas A069799(1500) = 5^2*3*2^3 = 600.

The first term that is different from A069799 is a(18). - Ivan Neretin, Jul 29 2015

Examples

			20 = 2^2*5, hence a(20) = 5^2*2 = 50.
		

Links

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

Crossrefs

Cf. A069799.

Cf. A027748, A124010, A089247, A071364, A046523.

Programs

Haskell

import Data.List (sort)
a085079 n = product $ zipWith (^) (a027748_row n) (sort $ a124010_row n)
-- Reinhard Zumkeller, Apr 27 2013

Mathematica

Table[Times @@ ((ar = Transpose[FactorInteger[n]])[[1]]^Sort[ar[[2]]]), {n, 70}] (* Ivan Neretin, Jul 29 2015*)
fise[n_]:=Module[{fi=FactorInteger[n]},Times@@(fi[[All,1]]^Sort[ fi[ [All,2]]])]; Array[fise,100] (* Harvey P. Dale, Sep 18 2017 *)

Formula

a(n) >= n. - Michel Marcus, Jul 30 2015

Extensions

Corrected and extended by Ray Chandler, Aug 17 2003