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%I #11 May 20 2015 06:00:23
%S 2,32,125,162,512,1250,2000,2592,4802,8192,10125,13122,20000,29282,
%T 32000,41472,49000,57122,76832,78125,92450,101250,131072,152881,
%U 162000,167042,207025,209952,215306,260642,300125,320000,388962,468512,512000,559682,663552
%N 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.
%C A subsequence of A000404.
%C 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.
%H Giovanni Resta, <a href="/A257965/b257965.txt">Table of n, a(n) for n = 1..526</a> (terms < 10^10)
%H Giovanni Resta, <a href="/A257965/a257965.txt">Decompositions for the first 526 terms</a>.
%t 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 *)
%o (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.
%K nonn
%O 1,1
%A _M. F. Hasler_, May 14 2015
%E Corrected and extended by _Giovanni Resta_, May 18 2015
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