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%I #33 Mar 03 2024 09:53:14
%S 1,2,3,5,3,7,5,11,13,7,5,17,19,7,11,23,13,29,5,31,11,17,7,37,19,13,41,
%T 7,43,23,47,17,53,11,19,29,59,61,31,13,11,67,23,7,71,73,37,11,13,79,
%U 41,83,17,43,29,89,13,31,47,19,97,101,17,103,7,53,107,109,11,37,113,19,23,59,17,61,41
%N Largest prime factor of the n-th squarefree number.
%H Reinhard Zumkeller, <a href="/A073482/b073482.txt">Table of n, a(n) for n = 1..10000</a>
%H Jean-Marie De Koninck and Rafael Jakimczuk, <a href="https://doi.org/10.33044/revuma.3154">Summing the largest prime factor over integer sequences</a>, Revista de la Unión Matemática Argentina, Vol. 67, No. 1 (2024), pp. 27-35.
%F a(n) = A006530(A005117(n)).
%F a(n) = A265668(n, A001221(n)). - _Reinhard Zumkeller_, Dec 13 2015
%F Sum_{A005117(n) <= x} a(n) = Sum_{i=1..k} d_i * x^2/log(x)^i + O(x^2/log(x)^(k+1)), for any given positive integer k, where d_i are constants, d_1 = 15/(2*Pi^2) = 0.759908... (A323669) (De Koninck and Jakimczuk, 2024). - _Amiram Eldar_, Mar 03 2024
%p issquarefree := proc(n::integer) local nf, ifa, lar; nf := op(2,ifactors(n)); for ifa from 1 to nops(nf) do lar := op(1,op(ifa,nf)); if op(2,op(ifa,nf)) >= 2 then RETURN(0); fi; od : RETURN(lar); end: printf("1,"); for n from 2 to 100 do lfa := issquarefree(n); if lfa > 0 then printf("%a,",lfa); fi; od : # _R. J. Mathar_, Apr 02 2006
%t FactorInteger[#][[-1, 1]]& /@ Select[Range[100], SquareFreeQ] (* _Jean-François Alcover_, Feb 01 2018 *)
%t s[n_] := Module[{f = FactorInteger[n]}, If[AllTrue[f[[;; , 2]], # < 2 &], f[[-1, 1]], Nothing]]; Array[s, 200] (* _Amiram Eldar_, Mar 03 2024 *)
%o (Haskell)
%o a073482 = a006530 . a005117 -- _Reinhard Zumkeller_, Feb 04 2012
%o (PARI) do(x)=my(v=List([1])); forfactored(n=2,x\1, if(vecmax(n[2][,2])==1, listput(v, vecmax(n[2][,1])))); Vec(v) \\ _Charles R Greathouse IV_, Nov 05 2017
%Y Cf. A073481, A001221, A005117, A006530, A265668, A323669.
%K nonn,easy
%O 1,2
%A _Reinhard Zumkeller_, Aug 03 2002
%E More terms from _Jason Earls_, Aug 06 2002
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