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

1,2

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) = A001222(A069459(n)).

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A001222, A069459, A069461, A069465.

Sequence in context: A249389 A016606 A341616 * A097469 A279727 A267092

Adjacent sequences: A069459 A069460 A069461 * A069463 A069464 A069465

Keyword

nonn

Author

Reinhard Zumkeller, Mar 24 2002

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

Status

approved