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%I #25 Sep 08 2022 08:46:20
%S 1,2,3,1,5,3,7,2,1,5,11,3,13,7,5,1,17,2,19,5,7,11,23,3,1,13,3,7,29,5,
%T 31,2,11,17,7,1,37,19,13,5,41,7,43,11,5,23,47,3,1,2,17,13,53,3,11,7,
%U 19,29,59,5,61,31,7,1,13,11,67,17,23,7,71,2,73,37
%N The greatest prime factor of the squarefree part of n, or 1 if n is square.
%H Alois P. Heinz, <a href="/A300518/b300518.txt">Table of n, a(n) for n = 1..20000</a>
%H Hugo Pfoertner, <a href="/A300518/a300518.pdf">Illustration of first 10^5 terms</a>, zoom into central part to see nice patterns.
%F a(n) = A006530(A007913(n)).
%e For n = 15000 = 5^4 * 3 * 2^3, 3 is the greatest unpaired prime, so a(15000) = 3.
%p a:= n-> max(1, seq(i[1]^irem(i[2], 2), i=ifactors(n)[2])):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Mar 07 2018
%t Array[FactorInteger[Sqrt[#] /. (c_: 1)*a_^(b_: 0) :> (c*a^b)^2][[-1, 1]] &, 74] (* _Michael De Vlieger_, Mar 10 2018, after _Bill Gosper_ at A007913 *)
%o (PARI) gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
%o a(n) = gpf(core(n)); \\ _Michel Marcus_, Mar 08 2018
%o (Magma) [#f eq 0 select 1 else f[#f][1] where f is Factorization(Squarefree(n)): n in [1..90]]; // _Vincenzo Librandi_, Mar 08 2018
%Y Cf. A006530, A007913.
%K nonn
%O 1,2
%A _Peter Kagey_, Mar 07 2018
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