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A056852 a(n) = (p^p + 1)/(p + 1), where p = prime(n). 3
7, 521, 102943, 23775972551, 21633936185161, 45957792327018709121, 98920982783015679456199, 870019499993663001431459704607, 85589538438707037818727607157700537549449, 533411691585101123706582594658103586126397951, 277766709362573247738903423315679814371773581141321037961 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
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)
LINKS
Lorenzo Sauras-Altuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).
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)
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 *)
CROSSREFS
Sequence in context: A080975 A003396 A124899 * A316394 A300391 A126196
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Aug 30 2000
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)