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%I #9 Sep 26 2020 13:42:41
%S 185527,451837,591751,1265471,1266929,1618973,1626227,1664713,2586277,
%T 2754683,2765519,2805193,3422303,3740309,3748499,4154779,5336479,
%U 5483953,5557987,6130151,6586091,7231013,7361801,7726571,8205553
%N Primes which are the sum of three distinct positive cubes of prime numbers in two or more distinct ways.
%H Chai Wah Wu, <a href="/A180099/b180099.txt">Table of n, a(n) for n = 1..10000</a>
%e 185527 = 47^3+43^3+13^3=53^3+31^3+19^3.
%t lst={};Do[Do[Do[If[PrimeQ[p=Prime[a]^3+Prime[b]^3+Prime[c]^3],AppendTo[lst,p]],{c,b-1,1,-1}],{b,a-1,1,-1}],{a,88}];lst1=Sort@lst; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst
%t Select[Tally[Select[Total/@Subsets[Prime[Range[50]]^3,{3}],PrimeQ]],#[[2]]> 1&] [[All,1]]//Sort (* _Harvey P. Dale_, Sep 26 2020 *)
%Y Cf. A011541, A024974, A025400, A122723, A180088, A180089.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 09 2010
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