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

1,1

Links

Table of n, a(n) for n=1..46.

Example

Prime(8) + 8 = 19 + 8 = 27 = 3^3.

Mathematica

f[n_] := Prime[n] + n; Select[Range[10^4], ! GCD @@ Last /@ FactorInteger[f[ # ]] == 1 &] (* Ray Chandler, May 21 2005 *)

Prog

(Sage) [n for n in (1..10000) if (n+nth_prime(n)).is_perfect_power()] # Giuseppe Coppoletta, Jun 08 2016

Crossrefs

Cf. A001597 (perfect powers), A107606 (associated prime(n)+n), A107607, A107608, A109314.

Sequence in context: A107792 A051206 A081451 * A109314 A319828 A325540

Adjacent sequences: A107602 A107603 A107604 * A107606 A107607 A107608

Keyword

nonn

Author

Zak Seidov, May 17 2005

Extensions

Extended by Ray Chandler, May 21 2005

Status

approved