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In prime factorization of n replace each prime power p^e with the greatest squarefree number <= p^e.
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%I #19 May 25 2023 13:20:51

%S 1,2,3,3,5,6,7,7,7,10,11,9,13,14,15,15,17,14,19,15,21,22,23,21,23,26,

%T 26,21,29,30,31,31,33,34,35,21,37,38,39,35,41,42,43,33,35,46,47,45,47,

%U 46,51,39,53,52,55,49,57,58,59,45,61,62,49,62,65,66,67,51,69,70,71,49,73

%N In prime factorization of n replace each prime power p^e with the greatest squarefree number <= p^e.

%C a(n)<=n and a(n)=n iff n is squarefree (A005117);

%C A081211(n)=a(a(n)), see A081212, A081213 and A081214 for iterations until a fix-point is reached.

%H R. Zumkeller, <a href="/A081210/b081210.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with p^e -> A070321(p^e), p prime.

%p A081210 := proc(n)

%p local a,pe;

%p a :=1 ;

%p for pe in ifactors(n)[2] do

%p a := a*A070321(op(1,pe)^op(2,pe)) ;

%p end do:

%p a ;

%p end proc:

%p seq(A081210(n),n=1..100) ; # _R. J. Mathar_, May 25 2023

%t gsf[n_] := For[k = n, True, k--, If[ SquareFreeQ[k], Return[k]]]; a[n_] := Times @@ gsf /@ Power @@@ FactorInteger[n]; Table[a[n], {n, 1, 80}] (* _Jean-François Alcover_, Mar 27 2013 *)

%K nonn,mult

%O 1,2

%A _Reinhard Zumkeller_, Mar 10 2003