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A107605 Numbers n such that prime(n) + n is a perfect power. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 13:13 EDT 2020. Contains 337380 sequences. (Running on oeis4.)