A344869 Number of distinct prime factors of n^n+1.

1, 1, 1, 2, 1, 3, 3, 3, 3, 4, 3, 6, 4, 5, 5, 6, 2, 3, 7, 5, 3, 6, 4, 8, 6, 7, 5, 11, 6, 7, 10, 7, 4, 11, 6, 13, 5, 7, 7, 8, 9, 6, 10, 8, 8, 14, 8, 10, 6, 7, 10, 11, 5, 8, 14, 11, 7, 13, 13, 9, 12, 8, 7, 18, 4, 12, 8, 7, 7, 16, 9, 8, 12, 4, 8, 24, 7, 9, 14, 7, 5, 12, 6, 12, 8, 13, 10, 12, 10, 6, 23, 15, 6, 9, 11, 16, 3, 8, 17, 23, 7

Offset: 0

Author

Seiichi Manyama, May 31 2021

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..148
• Eric Weisstein's World of Mathematics, Sierpinski Number of the First Kind.

Crossrefs

Cf. A001221, A014566, A085723, A128428, A344859, A344870.

Programs

Magma

[#PrimeDivisors(n^n+1): n in [0..100]];

Mathematica

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

PARI

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

Formula

a(n) = A001221(A014566(n)).

Extensions

a(67)-a(79) from Jon E. Schoenfield, May 31 2021

a(80)-a(100) from Seiichi Manyama, May 31 2021