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 A274247 Numbers n such that n^k is the sum of a positive square and a positive cube for all k not divisible by 6. 0
 12348, 16464, 433664, 444528, 617400, 790272, 1053696, 2534400, 2737152, 6585600, 6667920, 7024032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is sufficient to prove that the decomposition exists for k=1..5, because if n^k = a^2+b^3, then n^(k+6) = (n^3*a)^2 + (n^2*b)^3. LINKS Table of n, a(n) for n=1..12. EXAMPLE 12348 is a term since 12348 = 98^2 + 14^3, 12348^2 = 9604^2 + 392^3, 12348^3 = 1361367^2 + 3087^3, 12348^4 = 76236552^2 + 259308^3, 12348^5 = 11206773144^2 + 5445468^3. PROG (PARI) isA055394(n) = for(k=1, sqrtnint(n-1, 3), if(issquare(n-k^3), return(1))); 0 isok(n) = isA055394(n) && isA055394(n^2) && isA055394(n^3) && isA055394(n^4) && isA055394(n^5) CROSSREFS Cf. A055394. Sequence in context: A091341 A077298 A255964 * A045080 A238051 A234919 Adjacent sequences: A274244 A274245 A274246 * A274248 A274249 A274250 KEYWORD nonn,more AUTHOR Altug Alkan, Jun 16 2016 EXTENSIONS a(6)-a(12) from Giovanni Resta, Jun 18 2016 STATUS approved

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Last modified August 14 18:55 EDT 2024. Contains 375166 sequences. (Running on oeis4.)