

A130510


ABC conjecture: values of c in the list of "abchits".


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
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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 abchit. 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 ABChits, J. Numb. Theory, Volume 128, Issue 6, June 2008, pp. 18641873.
Noam D. Elkies, The ABC's of Number Theory, The Harvard College Mathematics Review, Vol. 1, No. 1, Spring 2007, pp. 5776.
Brian Hayes, Easy as abc
Wikipedia, abc conjecture


EXAMPLE

81 appears twice because 1+80=81 and 32+49=81 are two abchits.


MATHEMATICA

rad[n_] := If[n==1, 1, Times@@(Transpose[FactorInteger[n]][[1]])]; nn=1000; Do[If[ !PrimeQ[c], Do[b=ca; 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



