A107605 Numbers n such that prime(n) + n is a perfect power.
3, 5, 8, 9, 12, 86, 105, 147, 176, 214, 230, 241, 355, 412, 503, 696, 1065, 1147, 1170, 1273, 1334, 2021, 2455, 2600, 2660, 2772, 3299, 3332, 3365, 4417, 4861, 6288, 6478, 6572, 8115, 8858, 8905, 9229, 9380, 9590, 9692, 9749, 10501, 10829, 11338, 11633
Offset: 1
Keywords
Examples
Prime(8) + 8 = 19 + 8 = 27 = 3^3.
Programs
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Mathematica
f[n_] := Prime[n] + n; Select[Range[10^4], ! GCD @@ Last /@ FactorInteger[f[ # ]] == 1 &] (* Ray Chandler, May 21 2005 *)
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Sage
[n for n in (1..10000) if (n+nth_prime(n)).is_perfect_power()] # Giuseppe Coppoletta, Jun 08 2016
Extensions
Extended by Ray Chandler, May 21 2005