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