A165454 -id:A165454 - cp's OEIS frontend

A165455 Primes p such that p^2 is a sum of three distinct positive cubes.

53, 59, 71, 163, 167, 251, 523, 577, 613, 643, 773, 787, 811, 827, 863, 881, 883, 919, 937, 1097, 1117, 1301, 1567, 1607, 1709, 1777, 1867, 1873, 1877, 1889, 1931, 2161, 2237, 2309, 2447, 2521, 2591, 2647, 2687, 2719, 2843, 2897, 2969, 3011, 3079, 3163

Offset: 1

Vladimir Joseph Stephan Orlovsky, Sep 20 2009

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A161992, A165454.

lst={};Do[Do[Do[d=Sqrt[a^3+b^3+c^3];If[d<=834&&IntegerQ[d]&&PrimeQ[d], AppendTo[lst,d]],{c,b+1,5!,1}],{b,a+1,5!,1}],{a,5!}];Union@lst

A000040 INTERSECT A165454.

{p: p in A000040 and p^2 in A024975}. [R. J. Mathar, Oct 07 2009]

Extended beyond 827 by R. J. Mathar, Oct 07 2009

Title corrected by Jeppe Stig Nielsen, Jan 26 2015

A271826 Integers n such that n^2 = x^3 + y^3 + z^3, where x, y, z are positive integers, is soluble.

Original entry on oeis.org

6, 9, 15, 27, 48, 53, 59, 71, 72, 78, 84, 87, 90, 96, 98, 100, 116, 120, 121, 125, 134, 153, 162, 163, 167, 180, 188, 204, 213, 215, 216, 224, 225, 226, 230, 240, 242, 243, 244, 251, 253, 255, 262, 264, 279, 280, 287, 288, 289, 303, 314, 324, 330, 342

Offset: 1

Altug Alkan, Apr 15 2016

Intersection of A000290 and A003072.
Corresponding squares are 36, 81, 225, 729, 2304, 2809, 3481, 5041, ...
A165454 is a subsequence.
Terms that are not listed in A165454 are 9, 72, 100, 215, 243, 279, 289, ...

			6 is a term because 6^2 = 1^3 + 2^3 + 3^3.
9 is a term because 9^2 = 3^3 + 3^3 + 3^3.
15 is a term because 15^2 = 1^3 + 2^3 + 6^3.

Cf. A000290, A003072, A112474, A165454.

list(lim) = my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y), if(issquare(k+z^3), listput(v, round(sqrt(k+z^3))))))); Set(v);

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A165455 Primes p such that p^2 is a sum of three distinct positive cubes.

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A271826 Integers n such that n^2 = x^3 + y^3 + z^3, where x, y, z are positive integers, is soluble.

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