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

1,1

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A007531, A007947, A033931.

Sequence in context: A066714 A054436 A055522 * A147799 A071021 A279865

Adjacent sequences: A078634 A078635 A078636 * A078638 A078639 A078640

Keyword

nonn

Author

Jon Perry, Dec 12 2002

Status

approved