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A078637
a(n) = rad(n(n+1)(n+2)), where rad(m) is the largest squarefree number dividing m (see A007947).
3
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
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
KEYWORD
nonn
AUTHOR
Jon Perry, Dec 12 2002
STATUS
approved