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A053585 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = p_k^e_k. 20
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 (list; graph; refs; listen; history; text; internal format)
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}] (* Jean-Fran├žois 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: A229998 A067620 A294650 * A098988 A274346 A034699

Adjacent sequences:  A053582 A053583 A053584 * A053586 A053587 A053588

KEYWORD

nonn,easy,nice

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified November 23 00:33 EST 2017. Contains 295107 sequences.