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

1,2

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A069799.

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

Sequence in context: A225891 A295417 A293448 * A289234 A033000 A130573

Adjacent sequences: A085076 A085077 A085078 * A085080 A085081 A085082

Keyword

nonn

Author

Amarnath Murthy, Jul 01 2003

Extensions

Corrected and extended by Ray Chandler, Aug 17 2003

Status

approved