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

Offset: 1

Author

Jon Perry, Dec 12 2002

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A002378, A007947, A008683, A014601, A139131, A307868.

Programs

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 *)

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))", "))

Formula

From Reinhard Zumkeller, Aug 05 2003: (Start)

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. (End)

From Reinhard Zumkeller, Apr 10 2008: (Start)

a(A014601(n)) = A139131(A014601(n)).

a(n) = A139131(n) * A014695(n). (End)

From Amiram Eldar, Apr 04 2025: (Start)

a(n) = A007947(A002378(n)).

Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Product_{p prime} (1 - 2/(p*(p+1))) = 0.4716806... (A307868). (End)