A267477 Integers n such that n^2 = (x^3 + y^3) / 2 where x, y > 0, is soluble.
1, 6, 8, 27, 42, 48, 64, 78, 125, 147, 162, 196, 216, 336, 343, 384, 456, 512, 624, 722, 729, 750, 1000, 1050, 1134, 1176, 1296, 1331, 1342, 1568, 1573, 1674, 1694, 1728, 2028, 2058, 2106, 2197, 2366, 2387, 2450, 2522, 2646, 2688, 2744, 2899, 3072, 3087, 3211, 3375, 3648, 3698
Offset: 1
Examples
42 is a term because 42^2 = (11^3 + 13^3) / 2. 78 is a term because 78^2 = (1^3 + 23^3) / 2. 147 is a term because 147^2 = (7^3 + 35^3) / 2. 1573 is a term because 1573^2 = (77^3 + 165^3) / 2.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Select[Range@1000, Resolve@ Exists[{x, y}, And[Reduce[#^2 == (x^3 + y^3)/2, {x, y}, Integers], x > 0, y > 0]] &] (* Michael De Vlieger, Jan 16 2016 *) (* or, much faster: *) Select[Range@ 1000, {} != PowersRepresentations[#^2 2, 2, 3] &] (* Giovanni Resta, Nov 26 2018 *) -
PARI
T = thueinit('z^3+1); is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0; for(n=1, 1e4, if(is(2*n^2), print1(n, ", ")));
Comments