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Search: id:A130510
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| A130510 |
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ABC conjecture: values of c in the list of "abc-hits". |
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4
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Let rad(x) be the function that computes the square-free 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.
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REFERENCES
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See A120498
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1269 (for c up to 10^6)
Brian Hayes, Easy as abc
Noam D. Elkies, The ABC's of Number Theory, Harvard College Mathematics Review, Vol. 1, No. 1, Spring 2007.
Sander R. Dahmen, Lower bounds for numbers in ABC-hits, J. Numb. Theory 2007/2008 (in press).
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EXAMPLE
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81 appears twice because 1+80=81 and 32+49=81 are two abc-hits.
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MATHEMATICA
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rad[n_] := If[n==1, 1, Times@@(Transpose[FactorInteger[n]][[1]])]; nn=10000; 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}]
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CROSSREFS
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Cf. A120498 (unique values of c).
Sequence in context: A048547 A075433 A018833 this_sequence A120498 A063134 A027620
Adjacent sequences: A130507 A130508 A130509 this_sequence A130511 A130512 A130513
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 01 2007
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