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

9, 245, 128, 125, 32, 214375, 250, 1331, 2057, 2197, 2187, 5021875, 256, 658503, 85184, 6875, 5120, 148046893, 6144, 19683, 327701, 23882769, 2048, 1830125, 729, 3536405, 539, 50653, 19712, 75926359382399, 19683, 81, 2000033, 793071909, 4131, 313046875, 32805

Offset: 1

Author

Vladimir Letsko, Apr 23 2016

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Wikipedia, abc conjecture

Crossrefs

Cf. A272239 (corresponding values of b).

Cf. A272234 (analog of this sequence without assumption that n - the smallest element of the triple).

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

Cf. A225426 (triples of abc-hits).

Cf. A130512 (radicals of abc-hits).

Cf. A007947 (radicals).

Programs

Maple

rad:=n -> mul(i,i in factorset(n)):
min_c_for_a:=proc(n) local a,b,c,ra,rc;
for a to n do
ra:=rad(a):
for c from 2*a+1 do
if igcd(a,c)=1 then rc:=rad(c):
if ra*rc
				

Extensions

More terms from Jinyuan Wang, Jun 08 2022