A272236 Least positive integer b such that (n, b, n+b) is an abc-hit.

8, 243, 125, 121, 27, 214369, 243, 1, 2048, 2187, 2176, 5021863, 243, 658489, 85169, 6859, 5103, 148046875, 6125, 19663, 327680, 23882747, 2025, 1830101, 704, 3536379, 5, 50625, 19683, 75926359382369, 19652, 49, 2000000, 793071875, 4096, 313046839, 32768, 2366250289

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(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.

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

Cf. A272234 (corresponding values of c).

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: A221417 A351367 A351370 * A272239 A227319 A229544

Adjacent sequences: A272233 A272234 A272235 * A272237 A272238 A272239

Keyword

nonn

Author

Vladimir Letsko, Apr 23 2016

Extensions

More terms from Jinyuan Wang, Jun 08 2022

Status

approved