A078637 a(n) = rad(n(n+1)(n+2)), where rad(m) is the largest squarefree number dividing m (see A007947).

6, 6, 30, 30, 210, 42, 42, 30, 330, 330, 858, 546, 2730, 210, 510, 102, 1938, 570, 3990, 2310, 10626, 1518, 690, 390, 390, 546, 1218, 6090, 26970, 930, 2046, 1122, 39270, 3570, 7770, 4218, 54834, 7410, 15990, 8610, 74046, 19866, 14190, 7590, 32430, 6486

Offset: 1

Author

Jon Perry, Dec 12 2002

Keywords

• nonn

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007531, A007947, A033931.

Programs

Haskell

a078637 n = a007947 $ product [n..n+2] -- Reinhard Zumkeller, Jul 04 2012

Maple

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)

Mathematica

lsf[n_]:=Max[Select[Divisors[n],SquareFreeQ]]; lsf/@Table[n(n+1)(n+2),{n,50}] (* Harvey P. Dale, Oct 18 2020 *)
a[n_] := Times @@ Union @@ (FactorInteger[#][[;; , 1]] & /@ (n + {0, 1, 2})); Array[a, 50] (* Amiram Eldar, Jun 30 2022 *)

PARI

rad(n)=local(p,i); p=factor(n)[,1]; prod(i=1,length(p),p[i])
for (k=1,100,print1(rad(k*(k+1)*(k+2))","))

Formula

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

a(n) = A007947(A033931(n)). - Reinhard Zumkeller, Jul 04 2012

a(n) = A007947(A007531(n+2)). - Amiram Eldar, Jun 30 2022