cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Zak Seidov, May 17 2005

Keywords

Comments

Corresponding n's are in A107605.

Links

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

A107605 Numbers n such that prime(n) + n is a perfect power.

Original entry on oeis.org

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

Views

Author

Zak Seidov, May 17 2005

Keywords

Examples

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

Crossrefs

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

Programs

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

A107608 Perfect powers which have the form prime(n) - n for some n.

Original entry on oeis.org

1, 1, 25, 32, 125, 128, 441, 529, 729, 961, 1089, 1369, 2025, 2809, 3375, 4489, 4900, 4913, 9216, 10201, 10404, 12167, 16384, 17576, 18225, 20736, 27889, 31684, 34596, 35344, 38416, 38809, 39601, 40804, 46656, 47961, 60516, 61009, 63504, 65025
Offset: 1

Views

Author

Zak Seidov, May 17 2005

Keywords

Comments

Corresponding n's in A107607.

Crossrefs

Cf. A001597 (perfect powers), A107605, A107606, A107607 (associated n).

Programs

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

Formula

a(n) = prime(A107607(n)) - A107607(n).

Extensions

Extended by Ray Chandler, May 21 2005
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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