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A272240 Least positive integer c such that (n, c-n, c) is an abc-hit and n is the least number in the triple.

%I A272240 #20 Jun 09 2022 02:29:56
%S A272240 9,245,128,125,32,214375,250,1331,2057,2197,2187,5021875,256,658503,
%T A272240 85184,6875,5120,148046893,6144,19683,327701,23882769,2048,1830125,
%U A272240 729,3536405,539,50653,19712,75926359382399,19683,81,2000033,793071909,4131,313046875,32805
%N A272240 Least positive integer c such that (n, c-n, c) is an abc-hit and n is the least number in the triple.
%C A272240 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 A272240 Wikipedia, <a href="http://en.wikipedia.org/wiki/Abc_conjecture">abc conjecture</a>
%e A272240 a(8) = 1331 because rad(8*1323*1331) = 2*21*11 = 462 < 1331, hence (8, 1323, 1331) is an abc-hit and (8, c-8, c) isn't an abc-hit for every c satisfying unequalities c < 1331 and 8 < c-8.
%p A272240 rad:=n -> mul(i,i in factorset(n)):
%p A272240 min_c_for_a:=proc(n) local a,b,c,ra,rc;
%p A272240 for a to n do
%p A272240 ra:=rad(a):
%p A272240 for c from 2*a+1 do
%p A272240 if igcd(a,c)=1 then rc:=rad(c):
%p A272240 if ra*rc<c then b:=c-a:
%p A272240 if ra*rc*rad(b)<c then break fi fi fi od:
%p A272240 print([a,b,c]) od end;
%Y A272240 Cf. A272239 (corresponding values of b).
%Y A272240 Cf. A272234 (analog of this sequence without assumption that n - the smallest element of the triple).
%Y A272240 Cf. A120498, A130510 (possible values of c in abc-hits).
%Y A272240 Cf. A225426 (triples of abc-hits).
%Y A272240 Cf. A130512 (radicals of abc-hits).
%Y A272240 Cf. A007947 (radicals).
%K A272240 nonn
%O A272240 1,1
%A A272240 _Vladimir Letsko_, Apr 23 2016
%E A272240 More terms from _Jinyuan Wang_, Jun 08 2022