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%I #19 Aug 27 2020 05:41:49
%S 1,7,2269,4129151,30762501251,2239747210,27448639374405504361,
%T 2413133306001931169183743,382044091289242990177493431399,
%U 92389875896827641843360078,41175701028835553188828526348886198418157,251171485090270512606177135871202294053615
%N Smallest k such that k*n^5 + 1 is an n-th power.
%e a(3) = 2269 because 2269*3^5 + 1 = 551368 = 82^3.
%t a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^5], k++ ]; AppendTo[a, (k^n-1)/n^5], {n, 1, 20}]; a
%Y Cf. A076943, A193746, A216439, A216471.
%K nonn
%O 1,2
%A _Michel Lagneau_, Sep 10 2012
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