A225425 Number of "abc-hits" with c < 10^n.

1, 6, 31, 120, 418, 1268, 3499, 8987, 22316, 51677, 116978, 252856, 528275, 1075319, 2131671, 4119410, 7801334, 14482065

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.

The first 6 terms were computed using A130510. More terms were found on the Wikipedia page.

Links

Table of n, a(n) for n=1..18.

Wikipedia, abc conjecture

Example

The only solution under 10 is 1 + 8 = 9.

Crossrefs

Cf. A130510, A130511, A130512 (c, a, and rad(a*b*c)).

Cf. A225426 (a,b,c in one sequence).

Sequence in context: A166786 A003728 A216370 * A267890 A244199 A128568

Adjacent sequences: A225422 A225423 A225424 * A225426 A225427 A225428

Keyword

nonn,base,hard,more

Author

T. D. Noe, May 22 2013

Status

approved