A069462 Number of prime factors of prime(n)^n-1, with multiplicity.

0, 3, 3, 8, 4, 8, 5, 11, 6, 11, 7, 16, 7, 10, 9, 15, 5, 16, 4, 19, 12, 14, 4, 24, 11, 15, 15, 19, 9, 23, 5, 22, 12, 10, 11, 26, 9, 14, 8, 22, 5, 26, 5, 22, 18, 21, 6, 30, 9, 16, 11, 24, 13, 28, 17, 27, 10, 23, 8, 37, 7, 14, 16, 29, 12, 20, 11, 22, 14, 26, 9, 40

Offset: 1

Author

Reinhard Zumkeller, Mar 24 2002

Keywords

• nonn

Examples

			A000040(8)^8-1 = 19^8-1 = 16983563040 = 2^5*3^2*5*17*181*3833, therefore a(8) = 11 and A069461(8) = 6.
A000040(9)^9-1 = 23^9-1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 6 and A069461(9) = 6.
		

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.

Crossrefs

Cf. A001222, A069459, A069461, A069465.

Programs

Mathematica

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

PARI

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

Formula

a(n) = A001222(A069459(n)).

Extensions

More terms from Hugo Pfoertner, May 21 2004

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

a(53)-a(72) using factordb.com from Amiram Eldar, Feb 17 2020