%I #23 Jan 10 2021 11:01:47
%S 1,2,3,2,5,6,7,8,3,10,11,144,13,14,15,64,17,324,19,400,21,22,23,13824,
%T 5,26,27,784,29,27000,31,1024,33,34,35,279936,37,38,39,64000,41,74088,
%U 43,1936,2025,46,47,5308416,7,2500,51,2704,53,157464,55,175616,57
%N a(n) = Product_{d|n, d<n} d if n is composite, n otherwise.
%C a(n) = n if n is prime, otherwise a(n) = A007956(n);
%C a(A084116(n)) = A084116(n).
%H Reinhard Zumkeller, <a href="/A066729/b066729.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n^c(n) * ( Product_{d|n, d<n} d )^(1-c(n)), where c is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jan 10 2021
%t a[1] = 1; a[n_ /; PrimeQ[n]] := n; a[n_] := Times @@ Most[Divisors[n]]; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, May 28 2015 *)
%t Table[If[CompositeQ[n],Times@@Most[Divisors[n]],n],{n,60}] (* _Harvey P. Dale_, Jun 24 2016 *)
%o (Haskell)
%o a066729 n = if pds == [1] then n else product pds
%o where pds = a027751_row n
%o -- _Reinhard Zumkeller_, Jul 31 2014
%o (PARI) a(n) = my(pd = vecprod(divisors(n))); if (isprime(n), pd, pd/n); \\ _Michel Marcus_, Jan 09 2021
%Y Cf. A002033, A006881, A030514, A000040.
%Y Cf. A027751, A007956, A084116, A010051.
%K nonn,nice
%O 1,2
%A _Reinhard Zumkeller_, Jan 15 2002
%E Revised and data corrected by _Reinhard Zumkeller_, Jul 31 2014