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A272239
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Least positive integer b such that b > n and (n, b, n+b) is an abc-hit.
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2
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8, 243, 125, 121, 27, 214369, 243, 1323, 2048, 2187, 2176, 5021863, 243, 658489, 85169, 6859, 5103, 148046875, 6125, 19663, 327680, 23882747, 2025, 1830101, 704, 3536379, 512, 50625, 19683, 75926359382369, 19652, 49, 2000000, 793071875, 4096, 313046839, 32768
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(8) = 1323 because rad(8*1323*1331) = 2*21*11 = 462 < 1331, hence (8, 1323, 1331) is an abc-hit and (8, b, b+3) isn't an abc-hit for every b where 8 < b < 1323.
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MAPLE
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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;
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PROG
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(PARI) rad(x, y, z) = my(f=factor(x*y*z)[, 1]~); prod(i=1, #f, f[i])
is_abc_hit(x, y, z) = gcd(x, y)==1 && gcd(x, z)==1 && gcd(y, z)==1 && rad(x, y, z) < z
a(n) = my(b=n+1); while(!is_abc_hit(n, b, n+b), b++); b \\ Felix Fröhlich, May 08 2016
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CROSSREFS
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Cf. A272240 (corresponding values of c).
Cf. A272236 (analog of this sequence without assumption that n - the smallest element of the triple).
Cf. A130512 (radicals of abc-hits).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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