

A274012


Integers n such that n^3 is the average of a nonzero square and a nonzero fourth power.


1



1, 5, 16, 25, 26, 40, 41, 50, 80, 81, 125, 250, 256, 365, 386, 400, 405, 416, 425, 450, 457, 477, 625, 626, 640, 656, 800, 841, 845, 1000, 1125, 1153, 1210, 1225, 1280, 1296, 1681, 1825, 2000, 2025, 2057, 2106, 2197, 2312, 2401, 3042, 3125, 3240, 3250, 3321, 3362, 3400, 3625
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OFFSET

1,2


COMMENTS

Numbers n such that 2*n^3 = x^2 + y^4 where x and y are nonzero integers, is soluble.
Square terms of this sequence are 1, 16, 25, 81, 256, 400, 625, 841, 1225, 1296, 1681, 2025, 2401, ...
A000351, the powers of 5, is a subsequence.
If n is a term, then n * k^4 is a term; as 2*n^3 = x^4 + y^2, 2 * (n * k^4)^3 = (k^3 * x)^4 + (k^6 * y)^2. (End)


LINKS



EXAMPLE

5 is a term because 5^3 = (13^2 + 3^4) / 2.


PROG

(PARI) is(n) = for(x=1, (2*n) ^ 0.75, if(issquare(2*n^3  x^4)&&2*n^3x^4>0, return(1)); 0) \\ David A. Corneth, Jun 06 2016


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



