A078636 - OEIS

A078636

a(n) = rad(n*(n+1)).

2, 6, 6, 10, 30, 42, 14, 6, 30, 110, 66, 78, 182, 210, 30, 34, 102, 114, 190, 210, 462, 506, 138, 30, 130, 78, 42, 406, 870, 930, 62, 66, 1122, 1190, 210, 222, 1406, 1482, 390, 410, 1722, 1806, 946, 330, 690, 2162, 282, 42, 70, 510, 1326, 1378, 318, 330, 770, 798

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OFFSET

1,1

COMMENTS

a(A014601(n)) = A139131(A014601(n)); a(n) = A139131(n) * A014695(n). - Reinhard Zumkeller, Apr 10 2008

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = rad(n*(n+1)) = rad(n)*rad(n+1), mu(a(n)) = mu(rad(n*(n+1))) = mu(rad(n))*mu(rad(n+1)), where rad=A007947 and mu=A008683. - Reinhard Zumkeller, Aug 05 2003

EXAMPLE

a(3)=6 as rad(3*4)=rad(12)=rad(2*2*3)=2*3=6.

MAPLE

A078636 := proc(n)

A007947(n)*A007947(n+1) ;

end proc:

seq( A078636(n), n=1..10) ; # R. J. Mathar, Mar 15 2023

MATHEMATICA

rad[n_] := Times @@ FactorInteger[n][[All, 1]];

a[n_] := rad[n(n+1)];

Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 27 2024 *)

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))", "))

CROSSREFS

Cf. A007947.

Sequence in context: A102261 A245486 A147298 * A083482 A290701 A200579

Adjacent sequences: A078633 A078634 A078635 * A078637 A078638 A078639

KEYWORD

nonn

AUTHOR

Jon Perry, Dec 12 2002

STATUS

approved