A069461 Number of distinct prime factors of prime(n)^n-1.

0, 1, 2, 3, 3, 5, 2, 6, 6, 8, 7, 11, 5, 7, 9, 8, 5, 12, 4, 13, 8, 10, 4, 16, 7, 12, 12, 13, 6, 18, 4, 15, 10, 8, 10, 19, 8, 9, 8, 17, 5, 21, 5, 13, 16, 16, 6, 21, 9, 12, 9, 15, 10, 20, 9, 22, 9, 17, 7, 31, 7, 11, 13, 21, 9, 17, 11, 16, 14, 21, 5, 32, 7, 12, 16

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..96 (using factordb.com)

Dario Alpern, Factorization using the Elliptic Curve Method.

FactorDB, Status of 509^97-1.

Formula

a(n) = A001221(A069459(n)).

Example

A000040(8)^8-1 = 19^8 - 1 = 16983563040 = 2^5*3^2*5*17*181*3833, therefore a(8) = 6 and A069462(8) = 11.
A000040(9)^9-1 = 23^9-1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 6 and A069462(9) = 6.

Mathematica

Table[PrimeNu[Prime[n]^n - 1], {n, 1, 30}] (* Amiram Eldar, Feb 17 2020 *)

Prog

(PARI) for(n=1, 52, print1(omega(prime(n)^n-1)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

Crossrefs

Cf. A001221, A069459, A069462, A069464.

Sequence in context: A181483 A205130 A324799 * A329071 A232932 A252502

Adjacent sequences: A069458 A069459 A069460 * A069462 A069463 A069464

Keyword

nonn

Author

Reinhard Zumkeller, Mar 24 2002

Extensions

More terms from Hugo Pfoertner, May 18 2004

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

a(53)-a(75) using factordb.com from Amiram Eldar, Feb 17 2020

Status

approved