A342173 -id:A342173 - cp's OEIS frontend

A342174 Primes in A342173.

3, 11, 23, 43, 53, 71, 107, 229, 241, 269, 293, 313, 643, 701, 857, 883, 1109, 1361, 1601, 1693, 1697, 1721, 1867, 2267, 2621, 2719, 2767, 2789, 2971, 3067, 3137, 3169, 3529, 3533, 3557, 3739, 3767, 4007, 4093, 4139, 4153, 4219, 4337, 4423, 4447, 4451, 4517, 4663, 4787, 4943, 5279, 5387, 5501

Offset: 1

J. M. Bergot and Robert Israel, Mar 03 2021

nonn

			The first three primes in A342173 are a(1) = A342173(3) = 3, a(2) = A342173(5) = 11, and a(3) = A342173(8) = 23.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A342173.

f:= proc(n) local t, i, s;
  t:= ithprime(n);
  add(floor(t/ ithprime(i)), i=1..n-1)
end proc:
select(isprime, map(f,[$1..100]));

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

Robert G. Wilson v, Aug 30 2000

nonn

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)

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).

Cf. A001039, A055642, A129290, A342173, A343767.

a := n -> (ithprime(n)^ithprime(n)+1)/(ithprime(n)+1): # Lorenzo Sauras Altuzarra, Nov 27 2022

Table[ (Prime[ n ]^Prime[ n ] + 1)/(Prime[ n ] + 1), {n, 2, 11} ]
(#^#+1)/(#+1)&/@Prime[Range[2,20]] (* Harvey P. Dale, Apr 23 2015 *)

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)

cp's OEIS Frontend

A342174 Primes in A342173.

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