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.

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A056852 a(n) = (p^p + 1)/(p + 1), where p = prime(n).

Original entry on oeis.org

7, 521, 102943, 23775972551, 21633936185161, 45957792327018709121, 98920982783015679456199, 870019499993663001431459704607, 85589538438707037818727607157700537549449, 533411691585101123706582594658103586126397951, 277766709362573247738903423315679814371773581141321037961
Offset: 2

Views

Author

Robert G. Wilson v, Aug 30 2000

Keywords

Comments

From Lorenzo Sauras Altuzarra, Nov 27 2022: (Start)
Are all terms pairwise coprime? If so, they induce a permutation of the natural numbers, as Fermat numbers do (see A343767).
Are all terms squarefree?
A342173(n) <= length(a(n)) = A055642(a(n)) (the proof is due to Jinyuan Wang). (End)

Crossrefs

Programs

  • Maple
    a := n -> (ithprime(n)^ithprime(n)+1)/(ithprime(n)+1): # Lorenzo Sauras Altuzarra, Nov 27 2022
  • Mathematica
    Table[ (Prime[ n ]^Prime[ n ] + 1)/(Prime[ n ] + 1), {n, 2, 11} ]
    (#^#+1)/(#+1)&/@Prime[Range[2,20]] (* Harvey P. Dale, Apr 23 2015 *)

Formula

From Lorenzo Sauras Altuzarra, Nov 27 2022: (Start)
a(n) = Sum_{k=0..prime(n)-1} (-prime(n))^k.
a(n) = F(prime(n), 1)/F(prime(n), 0), where F(b, n) = b^b^n + 1 (i.e., F(b, n) is the n-th base-b Fermat number, see A129290). (End)
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