A053585 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = p_k^e_k.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 9, 19, 5, 7, 11, 23, 3, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 7, 9, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 49, 25, 17, 13, 53, 27, 11, 7, 19, 29, 59, 5, 61, 31, 7, 64, 13, 11, 67, 17, 23, 7, 71, 9, 73, 37, 25, 19, 11, 13, 79

Offset: 1

Author

Frederick Magata (frederick.magata(AT)uni-muenster.de), Jan 19 2000

Keywords

• nonn
• easy
• nice

Comments

Let p be the largest prime dividing n, a(n) is the largest power of p dividing n.

Examples

			a(42)=7 because 42=2*3*7, a(144)=9 because 144=16*9=2^4*3^2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A020639, A006530, A034684, A028233, A051119, A008475.

Different from A034699.

Programs

Haskell

a053585 = last . a141809_row  -- Reinhard Zumkeller, Jan 29 2013

Maple

a:= n-> `if`(n=1, 1, (i->i[1]^i[2])(sort(ifactors(n)[2])[-1])):
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 03 2023

Mathematica

Table[Power @@ Last @ FactorInteger @ n, {n, 79}] (* Jean-François Alcover, Apr 01 2011 *)

PARI

a(n)=if(n>1,my(f=factor(n)); f[#f~,1]^f[#f~,2],1) \\ Charles R Greathouse IV, Nov 10 2015

Python

from sympy import factorint, primefactors
def a(n):
    if n==1: return 1
    p = primefactors(n)[-1]
    return p**factorint(n)[p] # Indranil Ghosh, May 19 2017

Formula

a(n) = A006530(n)^A071178(n). - Reinhard Zumkeller, Aug 27 2011

a(n) = A141809(n,A001221(n)). - Reinhard Zumkeller, Jan 29 2013

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Apr 20 2000