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

9, 245, 128, 125, 32, 214375, 250, 9, 2057, 2197, 2187, 5021875, 256, 658503, 85184, 6875, 5120, 148046893, 6144, 19683, 327701, 23882769, 2048, 1830125, 729, 3536405, 32, 50653, 19712, 75926359382399, 19683, 81, 2000033, 793071909, 4131, 313046875, 32805, 2366250327

Offset

1,1

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.

Links

Table of n, a(n) for n=1..38.

Wikipedia, abc conjecture

Example

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.

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 a+1 do
if igcd(a, c)=1 then rc:=rad(c):
if ra*rc<c then b:=c-a:
if ra*rc*rad(b)<c then break fi fi fi od:
print([a, b, c]) od end;

Crossrefs

Cf. A272236 (corresponding values of b).

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).

Sequence in context: A183235 A359732 A259673 * A272240 A161159 A367541

Adjacent sequences: A272231 A272232 A272233 * A272235 A272236 A272237

Keyword

nonn

Author

Vladimir Letsko, Apr 23 2016

Extensions

More terms from Jinyuan Wang, Jun 08 2022

Status

approved