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One half of the radical (squarefree kernel) of the abc-triples (a=1, b(n) = A216323(n), c(n) = 1 + b(n)).
2

%I #16 Jan 05 2023 10:17:19

%S 3,21,21,15,105,33,51,57,195,195,273,465,205,285,987,105,1155,897,651,

%T 1365,105,357,1185,615,715,665,2345,4395,2037,1155,3003,897,1239,3255,

%U 2667,8463,5691,7755,2415,4305,11985,4123

%N One half of the radical (squarefree kernel) of the abc-triples (a=1, b(n) = A216323(n), c(n) = 1 + b(n)).

%C See a comment on A216323 for the definition of an abc-triple, radical r and quality q which is always > 1 by this definition. There also a link is given.

%H Wolfdieter Lang, <a href="/A216324/a216324_1.txt">Maple program for radical of a*b*(a+b) </a>.

%F a(n) = r(1,b(n),b(n)+1) with b(n) = A216323(n), n>=1, and r(a,b,c) is the radical, also known as squarefree kernel, of a*b*c.

%e 2*105 = 2*a(21) = r(1,4374,4375) = 1*6*35 = 210.

%p read "radabc.txt": [seq(radabc(1,A216324(n)),n=1..42)]/2;

%p (with the above given link with the maple text file)

%t rad[n_] := Times @@ Transpose[FactorInteger[n]][[1]]; a = 1; Table[t = {}; mx = 10^n; Do[c = a + b; If[c < mx && GCD[a, b] == 1 && Log[c] > Log[rad[a*b*c]], AppendTo[t, rad[b*c]/2]], {b, a, mx - a}], {n, 5}]; t (* _T. D. Noe_, Sep 24 2012 *)

%Y Cf. A216323.

%K nonn

%O 1,1

%A _Wolfdieter Lang_, Sep 24 2012