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a(n) = gcd(A046523(n), n).
3

%I #15 May 21 2017 14:31:58

%S 1,2,1,4,1,6,1,8,1,2,1,12,1,2,3,16,1,6,1,4,3,2,1,24,1,2,1,4,1,30,1,32,

%T 3,2,1,36,1,2,3,8,1,6,1,4,3,2,1,48,1,2,3,4,1,6,1,8,3,2,1,60,1,2,3,64,

%U 1,6,1,4,3,10,1,72,1,2,3,4,1,6,1,16,1,2,1,12,1,2,3,8,1,30,1,4,3,2,1,96,1,2

%N a(n) = gcd(A046523(n), n).

%H Antti Karttunen, <a href="/A083258/b083258.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[GCD[n, Times @@ MapIndexed[Prime[First[#2]]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]]], {n, 98}] (* _Michael De Vlieger_, May 21 2017 *)

%o (PARI)

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o A083258(n) = gcd(n,A046523(n)); \\ _Antti Karttunen_, May 21 2017

%Y Cf. A046523, A071364, A083255-A083260, A083261.

%K nonn

%O 1,2

%A _Labos Elemer_, May 09 2003