A107606 Perfect powers which have the form prime(n) + n for some n.

8, 16, 27, 32, 49, 529, 676, 1000, 1225, 1521, 1681, 1764, 2744, 3249, 4096, 5929, 9604, 10404, 10609, 11664, 12321, 19600, 24336, 25921, 26569, 27889, 33856, 34225, 34596, 46656, 51984, 68921, 71289, 72361, 91204, 100489, 101124, 104976

Offset: 1

Author

Zak Seidov, May 17 2005

Keywords

• nonn

Comments

Corresponding n's are in A107605.

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001597 (perfect powers), A107605 (associated n), A107607, A107608.

Programs

Mathematica

f[n_] := Prime[n] + n; Select[f /@ Range[10^4], ! GCD @@ Last /@ FactorInteger[ # ] == 1 &] (* Ray Chandler, May 21 2005 *)
perfPQ[n_]:=GCD@@FactorInteger[n][[All,2]]>1; Select[Table[Prime[n]+n,{n,10000}],perfPQ] (* Harvey P. Dale, Jan 28 2023 *)

Formula

A107606(n) = prime[A107605(n)] + A107605(n)

Extensions

Extended by Ray Chandler and Robert G. Wilson v, May 21 2005