# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a216324 Showing 1-1 of 1 %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, Maple program for radical of a*b*(a+b) . %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE