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%I A053585 #42 Nov 03 2023 06:50:21
%S A053585 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,
%T A053585 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,
%U A053585 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
%N A053585 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = p_k^e_k.
%C A053585 Let p be the largest prime dividing n, a(n) is the largest power of p dividing n.
%H A053585 Alois P. Heinz, <a href="/A053585/b053585.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%F A053585 a(n) = A006530(n)^A071178(n). - _Reinhard Zumkeller_, Aug 27 2011
%F A053585 a(n) = A141809(n,A001221(n)). - _Reinhard Zumkeller_, Jan 29 2013
%e A053585 a(42)=7 because 42=2*3*7, a(144)=9 because 144=16*9=2^4*3^2.
%p A053585 a:= n-> `if`(n=1, 1, (i->i[1]^i[2])(sort(ifactors(n)[2])[-1])):
%p A053585 seq(a(n), n=1..100);  # _Alois P. Heinz_, Nov 03 2023
%t A053585 Table[Power @@ Last @ FactorInteger @ n, {n, 79}] (* _Jean-François Alcover_, Apr 01 2011 *)
%o A053585 (Haskell)
%o A053585 a053585 = last . a141809_row  -- _Reinhard Zumkeller_, Jan 29 2013
%o A053585 (PARI) a(n)=if(n>1,my(f=factor(n)); f[#f~,1]^f[#f~,2],1) \\ _Charles R Greathouse IV_, Nov 10 2015
%o A053585 (Python)
%o A053585 from sympy import factorint, primefactors
%o A053585 def a(n):
%o A053585     if n==1: return 1
%o A053585     p = primefactors(n)[-1]
%o A053585     return p**factorint(n)[p] # _Indranil Ghosh_, May 19 2017
%Y A053585 Cf. A020639, A006530, A034684, A028233, A051119, A008475.
%Y A053585 Different from A034699.
%K A053585 nonn,easy,nice
%O A053585 1,2
%A A053585 Frederick Magata (frederick.magata(AT)uni-muenster.de), Jan 19 2000
%E A053585 More terms from Andrew Gacek (andrew(AT)dgi.net), Apr 20 2000

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