A078637 - OEIS

%I #26 Jun 30 2022 08:36:49

%S 6,6,30,30,210,42,42,30,330,330,858,546,2730,210,510,102,1938,570,

%T 3990,2310,10626,1518,690,390,390,546,1218,6090,26970,930,2046,1122,

%U 39270,3570,7770,4218,54834,7410,15990,8610,74046,19866,14190,7590,32430,6486

%N a(n) = rad(n(n+1)(n+2)), where rad(m) is the largest squarefree number dividing m (see A007947).

%H Reinhard Zumkeller, <a href="/A078637/b078637.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = rad(n)*rad(n+1)*rad(n+2) if n is odd; or rad(n/2)*rad(n+1)*rad(n/2+1) if n is even. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 13 2004

%F a(n) = A007947(A033931(n)). - _Reinhard Zumkeller_, Jul 04 2012

%F a(n) = A007947(A007531(n+2)). - _Amiram Eldar_, Jun 30 2022

%e a(3) = rad(3*4*5) = 30.

%p with(numtheory):rad:=proc(n) local s,i: s:=ifactors(n)[2]: RETURN(mul(s[i][1],i=1..nops(s))): end; seq(rad(n*(n+1)*(n+2)),n=1..60); seq(piecewise(n mod 2=0,rad(n/2)*rad(n+1)*rad(n/2+1),rad(n)*rad(n+1)*rad(n+2)),n=1..60); (C. Ronaldo)

%t lsf[n_]:=Max[Select[Divisors[n],SquareFreeQ]]; lsf/@Table[n(n+1)(n+2),{n,50}] (* _Harvey P. Dale_, Oct 18 2020 *)

%t a[n_] := Times @@ Union @@ (FactorInteger[#][[;; , 1]] & /@ (n + {0, 1, 2})); Array[a, 50] (* _Amiram Eldar_, Jun 30 2022 *)

%o (PARI) rad(n)=local(p,i); p=factor(n)[,1]; prod(i=1,length(p),p[i])

%o for (k=1,100,print1(rad(k*(k+1)*(k+2))","))

%o (Haskell)

%o a078637 n = a007947 $ product [n..n+2] -- _Reinhard Zumkeller_, Jul 04 2012

%Y Cf. A007531, A007947, A033931.

%K nonn

%O 1,1

%A _Jon Perry_, Dec 12 2002