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%I #6 May 23 2013 01:22:39
%S 1,8,9,5,27,32,1,48,49,1,63,64,1,80,81,32,49,81,4,121,125,3,125,128,1,
%T 224,225,1,242,243,2,243,245,7,243,250,13,243,256,81,175,256,1,288,
%U 289,100,243,343,32,343,375,5,507,512,169,343,512,1,512,513,27,512,539
%N The triples of numbers (a,b,c) that are "abc-hits".
%C Let rad(x) be the function that computes the squarefree kernel of x (see A007947). A triple {a,b,c} of positive integers with a+b=c, gcd(a,b)=1 and c > rad(a*b*c) is called an abc-hit.
%H T. D. Noe, <a href="/A225426/b225426.txt">Table of (a, b, c)(n), n = 1..1269</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Abc_conjecture">abc conjecture</a>
%t rad[n_] := If[n == 1, 1, Times @@ (Transpose[FactorInteger[n]][[1]])]; nn = 1000; t = {}; r = Table[rad[n], {n, nn}]; Do[If[! PrimeQ[c], Do[b = c - a; If[GCD[a, b] == 1 && r[[a]]*r[[b]]*r[[c]] < c, num++; AppendTo[t, {a, b, c}]], {a, c/2}]], {c, 2, nn}]; t
%Y Cf. A130510, A130511, A130512 (c, a, and rad(a*b*c)).
%Y Cf. A225425 (number of solutions with c < 10^n).
%K nonn
%O 1,2
%A _T. D. Noe_, May 22 2013
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