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 A297867 3-powerful numbers that can be written as the sum of two coprime 3-powerful numbers. 0
 776151559, 3518958160000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Any counterexample to the Beal conjecture, i.e., the statement that the Diophantine equation A^x + B^y = C^z has no solution for pairwise coprime A, B, C and x, y, z > 2, has to be a term from this sequence. LINKS A. Nitaj, On a conjecture of Erdős on 3-powerful numbers, Bull. London Math. Soc. 27 (1995), no. 4, 317-318. Wikipedia, Beal conjecture EXAMPLE 3518958160000 = 1392672604221 + 2126285555779 = 3^4 * 29^3 * 89^3 + 7^3 * 11^3 * 167^3 = 2^7 * 5^4 * 353^3. PROG (PARI) is_a036966(n) = my(e=factor(n)[, 2]~); if(#e==0 || vecmin(e) < 3, return(0)); 1 is(n) = if(!is_a036966(n), return(0)); my(x=1, y=n-1); while(x < y, if(gcd(x, y)==1 && n==x+y && is_a036966(x) && is_a036966(y), return(1)); x++; y--); 0 CROSSREFS Cf. A036966. Sequence in context: A118876 A157788 A058420 * A344729 A344730 A225389 Adjacent sequences:  A297864 A297865 A297866 * A297868 A297869 A297870 KEYWORD nonn,hard,bref,more AUTHOR Felix Fröhlich, Jan 07 2018 STATUS approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)