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 A120498 Numbers C from the ABC conjecture. 16
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS R. J. Mathar and T. D. Noe, Table of n, a(n) for n=1..868 Bart de Smit, Triples of small size [references the ABC@Home project which is inactive since 2015]. A. Granville and T. J. Tucker, It's As Easy As abc Abderrahmane Nitaj, The ABC Conjecture Home Page. Ivars Peterson, Math Trek, The Amazing ABC Conjecture [Internet Archive Wayback Machine] Eric Weisstein's World of Mathematics, abc conjecture Wikipedia, abc conjecture FORMULA A+B=C; gcd(A,B)=1; A007947(A*B*C) < C. EXAMPLE 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. MATHEMATICA rad[n_] := Times @@ First /@ FactorInteger[n]; isABC[a_, b_, c_] := (If[a + b != c || GCD[a, b] != 1, Return[0]]; r = rad[a*b*c]; If[r < c, Return[1], Return[0]]); isC[c_] := (For[a = 1, a <= Floor[c/2], a++, If[isABC[a, c - a, c] != 0, Return[1]]]; Return[0]); Select[Range[4000], isC[#] == 1 & ] (* Jean-François Alcover, Jun 24 2013, translated and adapted from Pari *) PROG (PARI) isABC(a, b, c)={ a+b==c && gcd(a, b)==1 && A007947(a*b*c)

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Last modified August 7 15:30 EDT 2020. Contains 336276 sequences. (Running on oeis4.)