%I #27 Jun 09 2022 02:23:12

%S 8,243,125,121,27,214369,243,1,2048,2187,2176,5021863,243,658489,

%T 85169,6859,5103,148046875,6125,19663,327680,23882747,2025,1830101,

%U 704,3536379,5,50625,19683,75926359382369,19652,49,2000000,793071875,4096,313046839,32768,2366250289

%N Least positive integer b such that (n, b, n+b) is an abc-hit.

%C 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 Wikipedia, <a href="http://en.wikipedia.org/wiki/Abc_conjecture">abc conjecture</a>

%e a(3) = 125 because rad(3*125*128) = 3*5*2 = 31 < 128, hence (3, 125, 128) is an abc-hit and (3, b, b+3) isn't an abc-hit for every b < 125.

%p rad:=n -> mul(i,i in factorset(n)):

%p min_c_for_a:=proc(n) local a,b,c,ra,rc;

%p for a to n do

%p ra:=rad(a):

%p for c from a+1 do

%p if igcd(a,c)=1 then rc:=rad(c):

%p if ra*rc<c then b:=c-a:

%p if ra*rc*rad(b)<c then break fi fi fi od:

%p print([a,b,c]) od end;

%Y Cf. A272239 (аnalog of this sequence taking into account that n - the smallest element of the triple).

%Y Cf. A272234 (corresponding values of c).

%Y Cf. A120498, A130510 (possible values of c in abc-hits).

%Y Cf. A225426 (triples of abc-hits).

%Y Cf. A130512 (radicals of abc-hits).

%Y Cf. A007947 (radicals).

%K nonn

%O 1,1

%A _Vladimir Letsko_, Apr 23 2016

%E More terms from _Jinyuan Wang_, Jun 08 2022