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%I #22 Jun 20 2016 06:01:51
%S 1,64,729,1000,1728,4096,13456,15625,27000,46656,59319,64000,110592,
%T 117649,148877,262144,531441,729000,777924,861184,1000000,1259712,
%U 1537600,1728000
%N Numbers n such that n^k is the average of a positive square and a positive cube for all k > 0.
%C Terms of this sequence are 1, 2^6, 3^6, 10^3, 12^3, 2^12, 116^2, 5^6, 30^3, ...
%e 13456 = 116^2 is a term because 13456 = (163^2 + 7^3) / 2, 13456^2 = (1088^2 + 712^3) / 2, 13456^3 = ((116^3)^2 + (116^2)^3) / 2, 13456^4 = (254426048^2 + 94192^3) / 2, 13456^5 = (1698254848^2 + 9580672^3) / 2, 13456^6 = ((116^6)^2 + (116^4)^3) / 2.
%o (PARI) isA055394(n) = for(k=1, sqrtnint(n-1, 3), if(issquare(n-k^3), return(1))); 0
%o isok(n) = isA055394(2*n) && isA055394(2*n^2) && isA055394(2*n^3) && isA055394(2*n^4) && isA055394(2*n^5)
%Y Cf. A055394.
%K nonn,more
%O 1,2
%A _Altug Alkan_, Jun 14 2016
%E a(13)-a(18) from _Giovanni Resta_, Jun 14 2016
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