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a(n) = rad(n*(n+1)).
3

%I #20 Mar 27 2024 10:43:00

%S 2,6,6,10,30,42,14,6,30,110,66,78,182,210,30,34,102,114,190,210,462,

%T 506,138,30,130,78,42,406,870,930,62,66,1122,1190,210,222,1406,1482,

%U 390,410,1722,1806,946,330,690,2162,282,42,70,510,1326,1378,318,330,770,798

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

%C a(A014601(n)) = A139131(A014601(n)); a(n) = A139131(n) * A014695(n). - _Reinhard Zumkeller_, Apr 10 2008

%H Reinhard Zumkeller, <a href="/A078636/b078636.txt">Table of n, a(n) for n = 1..1000</a>

%F 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

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

%p A078636 := proc(n)

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

%p end proc:

%p seq( A078636(n),n=1..10) ; # _R. J. Mathar_, Mar 15 2023

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

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

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Mar 27 2024 *)

%o (PARI) rad(n)=local(p,i); p=factor(n)[,1]; prod(i=1,length(p),p[i])

%o for (k=1,100,print1(rad(k*(k+1))", "))

%Y Cf. A007947.

%K nonn

%O 1,1

%A _Jon Perry_, Dec 12 2002