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%I #27 Oct 03 2019 03:11:53
%S 0,1,2,4,5,8,9,10,12,13,16,17,18,20,24,25,26,27,28,29,31,32,33,34,35,
%T 36,37,40,41,43,44,45,48,49,50,52,53,54,57,58,59,61,63,64,65,68,72,73,
%U 74,76,80,81,82,85,89,90,91,96,97,98,100,101,104,106,108,109,113,116,117
%N Numbers expressible as a^b + c^d with b&d > 1 and a&c >= 0.
%t mx = 120; s = {0,1} ~Join~ Select[Range[2, mx], GCD @@ (Last /@ FactorInteger[#]) > 1 &]; Union[ Reap[Do[v = s[[i]] + s[[j]]; If[v <= mx, Sow@v], {i, Length@s}, {j, i}]][[2, 1]]] (* _Giovanni Resta_, Sep 19 2019 *)
%o (PARI) upto(n)={my(p=(1 + x + sum(k=2, sqrtint(n), sum(e=2, logint(n,k), x^(k^e))) + O(x*x^n))^2); select(i->polcoef(p,i), [0..n])} \\ _Andrew Howroyd_, Sep 22 2019
%Y Cf. A070049.
%K nonn
%O 1,3
%A _Elan Roth_, Sep 18 2019
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