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A052126 a(1) = 1; for n>1, a(n)=n/(largest prime dividing n).

%I A052126 #41 Jul 02 2025 16:01:58
%S A052126 1,1,1,2,1,2,1,4,3,2,1,4,1,2,3,8,1,6,1,4,3,2,1,8,5,2,9,4,1,6,1,16,3,2,
%T A052126 5,12,1,2,3,8,1,6,1,4,9,2,1,16,7,10,3,4,1,18,5,8,3,2,1,12,1,2,9,32,5,
%U A052126 6,1,4,3,10,1,24,1,2,15,4,7,6,1,16,27,2,1,12,5,2,3,8,1,18,7,4,3,2,5,32,1
%N A052126 a(1) = 1; for n>1, a(n)=n/(largest prime dividing n).
%C A052126 For n>1, a(n)=1 if and only if n is prime. - _Zak Seidov_, Feb 09 2015
%C A052126 For n > 1, a(n) is the smallest divisor of n such that n/a(n) is prime. - _David James Sycamore_, Jan 03 2024
%H A052126 Reinhard Zumkeller, <a href="/A052126/b052126.txt">Table of n, a(n) for n = 1..10000</a>
%F A052126 a(n) = n/A006530(n).
%F A052126 a(n) = A130065(n)/A020639(n). - _Reinhard Zumkeller_, May 05 2007
%F A052126 a(A002110(n)) = A002110(n-1), a(p^k) = p^(k-1), p any prime; k >= 1. - _David James Sycamore_, Jan 03 2024
%F A052126 a(n) = n - A171462(n). - _Antti Karttunen_, Jan 04 2024
%e A052126 a(15) = 15/(largest prime dividing 15) = 15/5 = 3.
%p A052126 a := n -> `if`(n=1, 1, n/max(numtheory[factorset](n)));
%p A052126 seq(a(n), n=1..97); # _Peter Luschny_, Jul 28 2014
%t A052126 a052126[n_] := Array[If[n == 1, 1, #/FactorInteger[#][[-1]][[1]]] &, n]; a052126[97] (* _Michael De Vlieger_, Dec 21 2014 *)
%o A052126 (PARI) gpf(n)=my(f=factor(n)[,1]); f[#f]
%o A052126 a(n)=if(n<4,return(1)); n/gpf(n) \\ _Charles R Greathouse IV_, Apr 28 2015
%Y A052126 Cf. A000040, A006530, A020639, A032742, A130065, A171462, A322820, A322826 (rgs-transform), A329697, A331410.
%Y A052126 Left inverse of A253560.
%K A052126 nonn,look
%O A052126 1,4
%A A052126 _James Sellers_, Jan 21 2000