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%I #21 Feb 12 2023 03:14:29
%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,2,1,1,1,4,1,1,1,2,1,1,1,1,1,1,
%T 1,1,1,1,1,4,1,1,1,2,3,1,1,8,1,5,1,2,1,9,1,4,1,1,1,2,1,1,3,1,1,1,1,2,
%U 1,1,1,2,1,1,5,2,1,1,1,8,1,1,1,2,1,1,1,4,1,3,1,2,1,1,1,16,1,7,3,1,1,1,1,4
%N a(n) is n divided by the largest power of the squarefree kernel of n (A007947) which divides it.
%C a(n) divides A003557 but is not equal to it.
%H Antti Karttunen, <a href="/A062760/b062760.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n/(A007947(n)^A051904(n)).
%F a(n) = n/A062759(n). - _Amiram Eldar_, Feb 12 2023
%e n=1800: the squarefree kernel is 2*3*5 = 30 and 900 = 30^2 divides n, a(1800) = 2, the quotient of 1800/900.
%p f:= proc(n) local F,m,t;
%p F:= ifactors(n)[2];
%p m:= min(seq(t[2],t=F));
%p mul(t[1]^(t[2]-m),t=F)
%p end proc:
%p map(f, [$1..200]); # _Robert Israel_, Nov 03 2017
%t {1}~Join~Table[n/#^IntegerExponent[n, #] &@ Last@ Select[Divisors@ n, SquareFreeQ], {n, 2, 104}] (* _Michael De Vlieger_, Nov 02 2017 *)
%t a[n_] := Module[{f = FactorInteger[n], e}, e = Min[f[[;; , 2]]]; f[[;; , 2]] -= e; Times @@ Power @@@ f]; Array[a, 100] (* _Amiram Eldar_, Feb 12 2023 *)
%o (PARI)
%o A007947(n) = factorback(factorint(n)[, 1]); \\ _Andrew Lelechenko_, May 09 2014
%o A051904(n) = if(1==n,0,vecmin(factor(n)[, 2])); \\ After _Charles R Greathouse IV_'s code
%o A062760(n) = n/(A007947(n)^A051904(n)); \\ _Antti Karttunen_, Sep 23 2017
%Y Cf. A001694, A003557, A007947, A051904, A003557, A052485, A062759.
%Y Cf. A059404 (n such that a(n)>1), A072774 (n such that a(n)=1).
%K nonn
%O 1,12
%A _Labos Elemer_, Jul 16 2001
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