A057954 - OEIS

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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

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OFFSET

1,1

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

FORMULA

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

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

EXAMPLE

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

MATHEMATICA

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

PROG

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(7^n- 1):n in [1..85]]; // Marius A. Burtea, Feb 02 2020

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.

Sequence in context: A119733 A140869 A111570 * A155896 A060710 A271853

Adjacent sequences: A057951 A057952 A057953 * A057955 A057956 A057957

KEYWORD

nonn

AUTHOR

Patrick De Geest, Nov 15 2000

STATUS

approved