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A078637
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a(n) = rad(n(n+1)(n+2)), where rad(m) is the largest squarefree number dividing m (see A007947).
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3
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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
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OFFSET
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1,1
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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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
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EXAMPLE
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a(3) = rad(3*4*5) = 30.
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MAPLE
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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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A007531, A007947, A033931.
Sequence in context: A066714 A054436 A055522 * A147799 A071021 A279865
Adjacent sequences: A078634 A078635 A078636 * A078638 A078639 A078640
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KEYWORD
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nonn
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AUTHOR
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Jon Perry, Dec 12 2002
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STATUS
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approved
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