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A272234 Least positive integer c such that (n, c-n, c) is an abc-hit.

%I A272234 #28 Jun 09 2022 02:23:20
%S A272234 9,245,128,125,32,214375,250,9,2057,2197,2187,5021875,256,658503,
%T A272234 85184,6875,5120,148046893,6144,19683,327701,23882769,2048,1830125,
%U A272234 729,3536405,32,50653,19712,75926359382399,19683,81,2000033,793071909,4131,313046875,32805,2366250327
%N A272234 Least positive integer c such that (n, c-n, c) is an abc-hit.
%C A272234 An abc-hit is a triple of coprime positive integers a, b, c such that a + b = c and rad(abc) < c, where rad(n) is the largest squarefree number dividing n.
%H A272234 Wikipedia, <a href="http://en.wikipedia.org/wiki/Abc_conjecture">abc conjecture</a>
%e A272234 a(2) = 245 because rad(2*243*245) = 2*3*35 = 210 < 245, hence (2, 243, 245) is an abc-hit and (2, c-2, c) isn't an abc-triple for every c < 245.
%p A272234 rad:=n -> mul(i,i in factorset(n)):
%p A272234 min_c_for_a:=proc(n) local a,b,c,ra,rc;
%p A272234 for a to n do
%p A272234 ra:=rad(a):
%p A272234 for c from a+1 do
%p A272234 if igcd(a,c)=1 then rc:=rad(c):
%p A272234 if ra*rc<c then b:=c-a:
%p A272234 if ra*rc*rad(b)<c then break fi fi fi od:
%p A272234 print([a,b,c]) od end;
%Y A272234 Cf. A272236 (corresponding values of b).
%Y A272234 Cf. A120498, A130510 (possible values of c in abc-hits).
%Y A272234 Cf. A225426 (triples of abc-hits).
%Y A272234 Cf. A130512 (radicals of abc-hits).
%Y A272234 Cf. A007947 (radicals).
%K A272234 nonn
%O A272234 1,1
%A A272234 _Vladimir Letsko_, Apr 23 2016
%E A272234 More terms from _Jinyuan Wang_, Jun 08 2022