A344859 a(n) is the number of divisors of n^n + 1.

2, 2, 2, 6, 2, 8, 8, 16, 8, 16, 8, 96, 16, 32, 48, 160, 4, 12, 288, 48, 8, 64, 16, 512, 64, 128, 32, 3072, 64, 128, 1024, 384, 16, 2048, 64, 18432, 32, 128, 192, 512, 768, 64, 1024, 384, 256, 16384, 256, 2560, 64, 192, 1024, 3072, 32, 512, 16384, 4096, 128, 8192, 8192, 768, 4096, 256, 128, 1376256, 16

Offset: 0

Author

Seiichi Manyama, May 31 2021

Keywords

• nonn

Links

• Tyler Busby, Table of n, a(n) for n = 0..148 (terms 0..123 from Max Alekseyev)
• Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind

Crossrefs

Cf. A000005, A014566, A062319, A064144, A121270, A334167.

Cf. A007571 (Lpf), A055385 (lpf).

Programs

Mathematica

a[0] = 2; a[n_] := DivisorSigma[0, n^n + 1]; Array[a, 45, 0] (* Amiram Eldar, May 31 2021 *)

PARI

a(n) = numdiv(n^n+1);

Formula

a(n) = A000005(A014566(n)).