

A057934


Number of prime factors of 10^n + 1 (counted with multiplicity).


14



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
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OFFSET

1,3


COMMENTS

2^(a(2n)1)1 predicts the number of pairsolutions 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^(F1)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.
Carlos Rivera, Puzzle 104, The Prime Puzzles & Problems Connection.
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, A057935A057941, 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



