login
A081210
In prime factorization of n replace each prime power p^e with the greatest squarefree number <= p^e.
6
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, 26, 21, 29, 30, 31, 31, 33, 34, 35, 21, 37, 38, 39, 35, 41, 42, 43, 33, 35, 46, 47, 45, 47, 46, 51, 39, 53, 52, 55, 49, 57, 58, 59, 45, 61, 62, 49, 62, 65, 66, 67, 51, 69, 70, 71, 49, 73
OFFSET
1,2
COMMENTS
a(n)<=n and a(n)=n iff n is squarefree (A005117);
A081211(n)=a(a(n)), see A081212, A081213 and A081214 for iterations until a fix-point is reached.
LINKS
FORMULA
Multiplicative with p^e -> A070321(p^e), p prime.
MAPLE
A081210 := proc(n)
local a, pe;
a :=1 ;
for pe in ifactors(n)[2] do
a := a*A070321(op(1, pe)^op(2, pe)) ;
end do:
a ;
end proc:
seq(A081210(n), n=1..100) ; # R. J. Mathar, May 25 2023
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A187043 A081211 A081213 * A285719 A070321 A239904
KEYWORD
nonn,mult
AUTHOR
Reinhard Zumkeller, Mar 10 2003
STATUS
approved