cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A216324 One half of the radical (squarefree kernel) of the abc-triples (a=1, b(n) = A216323(n), c(n) = 1 + b(n)).

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%I A216324 #16 Jan 05 2023 10:17:19
%S A216324 3,21,21,15,105,33,51,57,195,195,273,465,205,285,987,105,1155,897,651,
%T A216324 1365,105,357,1185,615,715,665,2345,4395,2037,1155,3003,897,1239,3255,
%U A216324 2667,8463,5691,7755,2415,4305,11985,4123
%N A216324 One half of the radical (squarefree kernel) of the abc-triples (a=1, b(n) = A216323(n), c(n) = 1 + b(n)).
%C A216324 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 A216324 Wolfdieter Lang, <a href="/A216324/a216324_1.txt">Maple program for radical of a*b*(a+b) </a>.
%F A216324 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 A216324 2*105 = 2*a(21) = r(1,4374,4375) = 1*6*35 = 210.
%p A216324 read "radabc.txt": [seq(radabc(1,A216324(n)),n=1..42)]/2;
%p A216324 (with the above given link with the maple text file)
%t A216324 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 A216324 Cf. A216323.
%K A216324 nonn
%O A216324 1,1
%A A216324 _Wolfdieter Lang_, Sep 24 2012