login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130510 ABC conjecture: values of c in the list of "abc-hits". 14
9, 32, 49, 64, 81, 81, 125, 128, 225, 243, 245, 250, 256, 256, 289, 343, 375, 512, 512, 513, 539, 625, 625, 625, 676, 729, 729, 729, 729, 961, 968, 1025, 1029, 1216, 1331, 1331, 1331, 1369, 1587, 1681, 2048, 2048, 2048, 2057, 2187, 2187, 2187, 2197, 2197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 corresponding values of a and rad(a*b*c) are in the sequences A130511 and A130512.

REFERENCES

See A120498

LINKS

T. D. Noe, Table of n, a(n) for n=1..1269 (for c up to 10^6)

Sander R. Dahmen, Lower bounds for numbers of ABC-hits, J. Numb. Theory, Volume 128, Issue 6, June 2008, pp. 1864-1873.

Noam D. Elkies, The ABC's of Number Theory, The Harvard College Mathematics Review, Vol. 1, No. 1, Spring 2007, pp. 57-76.

Brian Hayes, Easy as abc

Wikipedia, abc conjecture

EXAMPLE

81 appears twice because 1+80=81 and 32+49=81 are two abc-hits.

MATHEMATICA

rad[n_] := If[n==1, 1, Times@@(Transpose[FactorInteger[n]][[1]])]; nn=1000; Do[If[ !PrimeQ[c], Do[b=c-a; If[GCD[a, b]==1 && rad[a*b*c]<c, Print[{a, b, c, rad[a*b*c]}]], {a, c/2}]], {c, 2, nn}]

CROSSREFS

Cf. A120498 (unique values of c).

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

Cf. A225425 (number of solutions with c < 10^n).

Cf. A225426 (triples of numbers a,b,c).

Sequence in context: A141573 A075433 A018833 * A120498 A155098 A063134

Adjacent sequences:  A130507 A130508 A130509 * A130511 A130512 A130513

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 01 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 06:49 EST 2020. Contains 338678 sequences. (Running on oeis4.)