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A272240 Least positive integer c such that (n, c-n, c) is an abc-hit and n is the least number in the triple. 1
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 (list; graph; refs; listen; history; text; internal format)
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..29.

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: A183235 A259673 A272234 * A161159 A300757 A289551

Adjacent sequences:  A272237 A272238 A272239 * A272241 A272242 A272243

KEYWORD

nonn,more

AUTHOR

Vladimir Letsko, Apr 23 2016

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)