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

1,1

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..37.

Wikipedia, abc conjecture

Example

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.

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<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. 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).

Sequence in context: A359732 A259673 A272234 * A161159 A367541 A300757

Adjacent sequences: A272237 A272238 A272239 * A272241 A272242 A272243

Keyword

nonn

Author

Vladimir Letsko, Apr 23 2016

Extensions

More terms from Jinyuan Wang, Jun 08 2022

Status

approved