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%I #20 Jun 08 2016 02:37:52
%S 1,162,324,3888,11664,18750,31250,32768,38416,40000,160000,167042,
%T 168750,253125,373248,607500,911250,1037232
%N Numbers n such that n^4 is the average of a positive cube and a positive fifth power.
%C Numbers n such that 2*n^4 is of the form x^3 + y^5 where x and y are positive integers.
%C Sequence is infinite because if m is a term, that is m^4 = (w^3 + z^5)/2 with w and z positive integers, then m*t^15 is also a term for every integer t>1. In fact: (m*t^15)^4 = ((w*t^20)^3 + (z*t^12)^5)/2.
%e 162 = 3*54 is a term because (3*54)^4 = ((18*54)^3 + 54^5)/2.
%e 38416 = 14^4 is a term because (14^4)^4 = ((3*14^5)^3 + (14^3)^5)/2.
%o (PARI) isA100293(n) = for(y=1, sqrtnint(n-1, 5), if(ispower(n-y^5, 3), return(1))); 0;
%o lista(nn) = for(n=1, nn, if(isA100293(2*n^4), print1(n, ", ")));
%Y Cf. A000583, A100293.
%K nonn,more
%O 1,2
%A _Altug Alkan_, Jun 07 2016
%E a(11)-a(18) from _Giovanni Resta_, Jun 07 2016
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