|
|
A225426
|
|
The triples of numbers (a,b,c) that are "abc-hits".
|
|
10
|
|
|
1, 8, 9, 5, 27, 32, 1, 48, 49, 1, 63, 64, 1, 80, 81, 32, 49, 81, 4, 121, 125, 3, 125, 128, 1, 224, 225, 1, 242, 243, 2, 243, 245, 7, 243, 250, 13, 243, 256, 81, 175, 256, 1, 288, 289, 100, 243, 343, 32, 343, 375, 5, 507, 512, 169, 343, 512, 1, 512, 513, 27, 512, 539
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Let rad(x) be the function that computes the squarefree kernel of x (see A007947). A triple {a,b,c} of positive integers with a+b=c, gcd(a,b)=1 and c > rad(a*b*c) is called an abc-hit.
|
|
LINKS
|
|
|
MATHEMATICA
|
rad[n_] := If[n == 1, 1, Times @@ (Transpose[FactorInteger[n]][[1]])]; nn = 1000; t = {}; r = Table[rad[n], {n, nn}]; Do[If[! PrimeQ[c], Do[b = c - a; If[GCD[a, b] == 1 && r[[a]]*r[[b]]*r[[c]] < c, num++; AppendTo[t, {a, b, c}]], {a, c/2}]], {c, 2, nn}]; t
|
|
CROSSREFS
|
Cf. A225425 (number of solutions with c < 10^n).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|