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

1, 882850585445281, 28084773172609134470952326813135521948919663474715912134590894817085103016117634792155856629828598766188378241

Offset

2,2

Comments

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

Links

Table of n, a(n) for n=2..4.

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

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A122000, A014566, A081216, A056009.

Sequence in context: A129935 A173405 A104835 * A346569 A349029 A384361

Adjacent sequences: A128443 A128444 A128445 * A128447 A128448 A128449

Keyword

bref,nonn

Author

Alexander Adamchuk, Mar 03 2007

Status

approved