A057936 - OEIS

A057936

Number of prime factors of 8^n + 1 (counted with multiplicity).

2, 2, 4, 2, 4, 4, 4, 3, 6, 6, 5, 4, 4, 6, 7, 3, 6, 6, 5, 4, 7, 6, 5, 5, 7, 10, 10, 5, 5, 11, 5, 3, 9, 9, 11, 6, 7, 8, 7, 6, 7, 10, 6, 7, 12, 8, 7, 7, 7, 14, 11, 5, 6, 10, 12, 8, 9, 8, 8, 8, 4, 9, 13, 4, 11, 12, 8, 9, 8, 15, 8, 8, 6, 10, 12, 8, 12, 17, 6, 7, 15, 10, 9, 12, 12, 10, 11, 8, 8, 18, 12

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OFFSET

1,1

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..502 (first 354 terms from Amiram Eldar)

S. S. Wagstaff, Jr., The Cunningham Project

FORMULA

a(n) = A057953(2n) - A057953(n). - T. D. Noe, Jun 19 2003

a(n) = A001222(A062395(n)) = A054992(3*n). - Amiram Eldar, Feb 02 2020

MATHEMATICA

PrimeOmega[8^Range[100]+1] (* Harvey P. Dale, Dec 16 2014 *)

PROG

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(8^n + 1):n in [1..110]]; // Marius A. Burtea, Feb 02 2020

CROSSREFS

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), this sequence (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A057953, A062395, A274905.

Sequence in context: A100008 A102763 A054844 * A033097 A036845 A094269

Adjacent sequences: A057933 A057934 A057935 * A057937 A057938 A057939

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 15 2000

STATUS

approved