A057954 Number of prime factors of 7^n - 1 (counted with multiplicity).

2, 5, 4, 8, 3, 8, 4, 10, 7, 8, 4, 13, 3, 9, 7, 13, 4, 12, 4, 14, 7, 9, 5, 18, 5, 8, 12, 13, 5, 14, 5, 16, 9, 8, 7, 18, 5, 9, 8, 18, 5, 15, 4, 15, 12, 9, 4, 22, 8, 11, 10, 13, 5, 18, 6, 19, 10, 9, 6, 24, 6, 11, 11, 20, 9, 17, 6, 14, 10, 18, 4, 26, 7, 10, 11, 13, 9, 17, 4, 24, 17, 12, 9, 22

Offset: 1

Author

Patrick De Geest, Nov 15 2000

Keywords

• nonn

Examples

			7^8-1 = 5764800 = 2^6 * 3 * 5^2 * 1201 and a(8) = bigomega(5764800) = 6+1+2+1 = 10. - _Bernard Schott_, Feb 02 2020
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..388 (first 378 terms from Amiram Eldar)
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

bigomega(b^n-1): A057951 (b=10), A057952 (b=9), A057953 (b=8), this sequence (b=7), A057955 (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A024075, A059889, A074249, A085032.

Programs

Magma

f:=func; [f(7^n- 1):n in [1..85]]; // Marius A. Burtea, Feb 02 2020

Mathematica

PrimeOmega[Table[7^n - 1, {n, 1, 30}]] (* Amiram Eldar, Feb 02 2020 *)

Formula

Möbius transform of A085032. - T. D. Noe, Jun 19 2003

a(n) = A001222(A024075(n)). - Amiram Eldar, Feb 02 2020