A056852 a(n) = (p^p + 1)/(p + 1), where p = prime(n).
7, 521, 102943, 23775972551, 21633936185161, 45957792327018709121, 98920982783015679456199, 870019499993663001431459704607, 85589538438707037818727607157700537549449, 533411691585101123706582594658103586126397951, 277766709362573247738903423315679814371773581141321037961
Offset: 2
Keywords
Links
- T. D. Noe, Table of n, a(n) for n = 2..26
- Lorenzo Sauras-Altuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).
Programs
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Maple
a := n -> (ithprime(n)^ithprime(n)+1)/(ithprime(n)+1): # Lorenzo Sauras Altuzarra, Nov 27 2022
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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)
Comments