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Search: id:A120498
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| A120498 |
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Numbers C of the ABC conjecture. |
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+0
4
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| 9, 32, 49, 64, 81, 125, 128, 225, 243, 245, 250, 256, 289, 343, 375, 512, 513, 539, 625, 676, 729, 961, 968, 1025, 1029, 1216, 1331, 1369, 1587, 1681, 2048, 2057, 2187, 2197, 2304, 2312, 2401, 2500, 2673, 3025, 3072, 3125, 3136, 3211, 3481, 3584, 3773, 3888
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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C-values are not repeated: (A,B,C)=(13,243,256) and (A,B,C)=(81,175,256) are only represented once, by 256, in the list, for example.
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LINKS
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R. J. Mathar and T. D. Noe, Table of n, a(n) for n=1..868
N. A. Carella, Note on the ABC Conjecture, math.NT/0606221.
A. Granville & T. J. Tucker, It's As Easy As abc
A. Nitaj, ABC Home Page.
I. Peterson, Math Trek, The Amazing ABC Conjecture
B. de Smit, ABC @ home.
Eric Weisstein's World of Mathematics, abc conjecture
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FORMULA
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A+B=C; gcd(A,B)=1; A007947(A*B*C)<C
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EXAMPLE
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For A=1, B=63 and C=64, C=64 is in the list because 1 and 63 are coprime,
because the set of prime factors of 1,63=3^2*7 and 64=2^6 has the product
of prime factors 3*2*7=42 and this product is smaller than 64.
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PROGRAM
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(PARI) A007947(n)= { local(p) ; p=factor(n)[, 1]; return(prod(i=1, length(p), p[i])) ; } isABC(a, b, c)= { local(r) ; if (a+b!=c || gcd(a, b) != 1, return(0) ); r=A007947(a*b*c) ; if(r<c, return(1), return(0) ; ) ; } isC(c)= { for(a=1, floor(c/2), if( isABC(a, c-a, c) != 0, return(1) ) ; ) ; return(0) ; } { for(n=1, 6000, if( isC(n), print1(n, ", ") ) ; ) }
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CROSSREFS
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Cf. A007947, A085152, A085153.
Cf. A130510 (values of c in the list of "abc-hits")
Sequence in context: A075433 A018833 A130510 this_sequence A155098 A063134 A152619
Adjacent sequences: A120495 A120496 A120497 this_sequence A120499 A120500 A120501
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 06 2006
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