

A053585


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


22



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
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OFFSET

1,2


COMMENTS

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


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A006530(n)^A071178(n).  Reinhard Zumkeller, Aug 27 2011
a(n) = A141809(n,A001221(n)).  Reinhard Zumkeller, Jan 29 2013


EXAMPLE

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


MATHEMATICA

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


PROG

(Haskell)
a053585 = last . a141809_row  Reinhard Zumkeller, Jan 29 2013
(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


CROSSREFS

Cf. A020639, A006530, A034684, A028233, A053585, A051119, A008475.
Different from A034699.
Sequence in context: A067620 A319677 A294650 * A305007 A098988 A274346
Adjacent sequences: A053582 A053583 A053584 * A053586 A053587 A053588


KEYWORD

nonn,easy,nice


AUTHOR

Frederick Magata (frederick.magata(AT)unimuenster.de), Jan 19 2000


EXTENSIONS

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


STATUS

approved



