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A057934 Number of prime factors of 10^n + 1 (counted with multiplicity). 13
1, 1, 3, 2, 2, 2, 2, 2, 5, 3, 5, 3, 3, 4, 7, 5, 4, 3, 2, 4, 8, 4, 5, 3, 5, 3, 7, 4, 3, 7, 2, 4, 9, 4, 5, 6, 4, 3, 10, 4, 3, 7, 4, 4, 12, 4, 4, 9, 4, 7, 8, 4, 2, 6, 10, 5, 6, 5, 4, 6, 3, 3, 12, 3, 6, 8, 2, 4, 10, 11, 3, 5, 4, 7, 11, 6, 12, 7, 4, 9, 11, 3, 7, 8, 8, 3, 8, 4, 4, 11, 6, 4, 8, 4, 6, 8, 4, 5, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

2^(a(2n)-1)-1 predicts the number of pair_solutions of even length L for AB = A^2 + B^2. For instance with length 18 we have 10^18 + 1 = 101.9901.999999000001 or 3 divisors F which when put into the Mersenne formula 2^(F-1)-1 yields 3 pairs (see reference 'Puzzle 104' for details).

LINKS

Ray Chandler, Table of n, a(n) for n = 1..310 (from Kamada link)

Makoto Kamada, Factorizations of 100...001.

C. Rivera, Puzzle 104

S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.

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

FORMULA

a(n) = A057951(2n) - A057951(n) - T. D. Noe, Jun 19 2003

PROG

(PARI) a(n)=bigomega(10^n+1) \\ Charles R Greathouse IV, Sep 14 2015

CROSSREFS

Cf. A003021, A001271, A046053, A057935-A057941, A054992, A001562, A057951.

Sequence in context: A174550 A119704 A104223 * A058758 A122396 A272893

Adjacent sequences:  A057931 A057932 A057933 * A057935 A057936 A057937

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 15 2000.

STATUS

approved

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Last modified August 18 16:13 EDT 2018. Contains 313833 sequences. (Running on oeis4.)