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Numbers that are the sum of 3 positive cubes in more than one way.
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%I #40 Aug 05 2021 15:28:50

%S 251,1009,1366,1457,1459,1520,1730,1737,1756,1763,1793,1854,1945,2008,

%T 2072,2241,2414,2456,2458,2729,2736,3060,3391,3457,3592,3599,3655,

%U 3745,3926,4105,4112,4131,4168,4229,4320,4376,4402,4437,4447

%N Numbers that are the sum of 3 positive cubes in more than one way.

%C Of course reordering the terms does not count.

%C A025456(a(n)) > 1. [_Reinhard Zumkeller_, Apr 23 2009]

%H T. D. Noe and Christian N. K. Anderson, <a href="/A008917/b008917.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms are from T. D. Noe)

%H Christian N. K. Anderson, <a href="/A008917/a008917.txt">Decomposition</a> of first 10000 terms into multiple cube triples.

%e a(2) = 1009 = 1^3+2^3+10^3 = 4^3+6^3+9^3.

%t Select[Range[4450], 1 < Length @ Cases[PowersRepresentations[#, 3, 3], {_?Positive, _?Positive, _?Positive}] &] (* _Jean-François Alcover_, Apr 04 2011 *)

%o (PARI) is(n)=k=ceil((n-2)^(1/3)); d=0; for(a=1, k, for(b=a, k, for(c=b, k, if(a^3+b^3+c^3==n, d++)))); d

%o n=3; while(n<5000, if(is(n)>1, print1(n, ", ")); n++) \\ _Derek Orr_, Aug 27 2015

%Y Cf. A001235, A003072, A024796, A025396, A025398, A025406, A309762.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_ and _J. H. Conway_