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A257965
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Numbers n such that n^3 = a^2 + b^2 and a^3 + b^3 is a square, for some positive integers a and b.
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1
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2, 32, 125, 162, 512, 1250, 2000, 2592, 4802, 8192, 10125, 13122, 20000, 29282, 32000, 41472, 49000, 57122, 76832, 78125, 92450, 101250, 131072, 152881, 162000, 167042, 207025, 209952, 215306, 260642, 300125, 320000, 388962, 468512, 512000, 559682, 663552
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OFFSET
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1,1
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COMMENTS
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A subsequence of A000404.
Two subsequences are given by: n = 2*m^4 with a = b = 2*m^6, and n = 5^3*m^4 with a = 5^4*m^6, b = 2*a.
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 1..526 (terms < 10^10)
Giovanni Resta, Decompositions for the first 526 terms.
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MATHEMATICA
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L = {}; n = 0; Clear[x, y]; While[n < 5000, n++; If[ And @@ (EvenQ /@ Last /@ Select[FactorInteger[n], Mod[First[#] + 1, 4] == 0 &]) && False =!= (sol = Reduce[n^3 == x^2 + y^2 && x >= y > 0, {x, y}, Integers]), ss = {x, y} /. List@ToRules@sol; If[{} != Select[ss, IntegerQ@ Sqrt@ Total[#^3] &, 1], AppendTo[L, n]; Print@L]]]; L (* Giovanni Resta, May 18 2015 *)
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PROG
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(PARI) is(n)={is_A000404(n)&&for(i=1, #T=sum2sqr(n^3), T[i][1]&&issquare(T[i][1]^3+T[i][2]^3)&&return(T[i]))} \\ Uses sum2sqr(), cf. A133388. Returns [a, b] if n is in the sequence, 0 else.
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CROSSREFS
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Sequence in context: A122127 A303078 A226395 * A191997 A274654 A112850
Adjacent sequences: A257962 A257963 A257964 * A257966 A257967 A257968
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler, May 14 2015
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EXTENSIONS
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Corrected and extended by Giovanni Resta, May 18 2015
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STATUS
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approved
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