A014566 -id:A014566 - cp's OEIS frontend

A085603 (2n)^(2n) + 1.

2, 5, 257, 46657, 16777217, 10000000001, 8916100448257, 11112006825558017, 18446744073709551617, 39346408075296537575425, 104857600000000000000000001

Offset: 0

Cino Hilliard, Jul 07 2003

a(n) is never a perfect square because (2n)^(2n) is a positive square and the only squares that differ by 1 are 0 and 1. Sierpinski numbers are n^n+1. Hence this sequence is a subset of the Sierpinski numbers (A014566). - T. D. Noe, Mar 31 2006

PARI
```
forstep(x=0,20,2,print1(x^x+1" "))
```

A128446 Quotients A122000(p-1) / (2^p - 1), where p = prime(n) for n > 1.

Original entry on oeis.org

1, 882850585445281, 28084773172609134470952326813135521948919663474715912134590894817085103016117634792155856629828598766188378241

Offset: 2

Alexander Adamchuk, Mar 03 2007

A014566(n) = n^n + 1 is a Sierpinski Number of the First Kind.
A014566(2^n - 1) is divisible by 2^n.
A122000(n) = ((2^n - 1)^(2^n - 1) + 1) / 2^n = A014566(2^n - 1) / 2^n = A081216(2^n - 1).
a(5) = 6.044...*10^3072, and is too large to include. - Amiram Eldar, Jul 17 2025

Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind.

Cf. A122000, A014566, A081216, A056009.

a[n_] := Module[{p = Prime[n]}, ((2^(p-1) - 1)^(2^(p-1) - 1) + 1)/(2^(p-1)*(2^p-1))]; Array[a, 3, 2] (* Amiram Eldar, Jul 17 2025 *)

a(n) = ((2^(prime(n)-1) - 1)^(2^(prime(n)-1)-1) + 1)/(2^(prime(n)-1)*(2^prime(n)-1)).

A180341 a(n) = k is the smallest number such that n is the number of distinct primes dividing k^k + 1.

Original entry on oeis.org

0, 3, 5, 9, 13, 11, 18, 23, 40, 30, 27, 60, 35, 45, 91, 69, 98, 63, 119

Offset: 1

Michel Lagneau, Jan 18 2011

			a(6) = 11 because the 6 distinct primes dividing 11^11 + 1 = 285311670612 are
  {2, 3, 23, 89, 199, 58367}.

Cf. A014566.

with(numtheory):for n from 1 to 8 do:ind:=0:for k from 1 to 40 while(ind=0)
  do: x:=k^k+1:y:=nops(factorset(x)):if y=n then ind:=1:printf(`%d, `,k):else
  fi:od: od:

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A085603 (2n)^(2n) + 1.

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A128446 Quotients A122000(p-1) / (2^p - 1), where p = prime(n) for n > 1.

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A180341 a(n) = k is the smallest number such that n is the number of distinct primes dividing k^k + 1.

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