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A057934 Number of prime factors of 10^n + 1 (counted with multiplicity). 14


%S 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,

%T 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,

%U 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

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

%C 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).

%H Ray Chandler, <a href="/A057934/b057934.txt">Table of n, a(n) for n = 1..310</a> (from Kamada link)

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit/10001.htm">Factorizations of 100...001</a>.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_104.htm">Puzzle 104</a>, The Prime Puzzles & Problems Connection.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/">Main Tables</a> from the Cunningham Project.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>

%F a(n) = A057951(2n) - A057951(n). - _T. D. Noe_, Jun 19 2003

%o (PARI) a(n)=bigomega(10^n+1) \\ _Charles R Greathouse IV_, Sep 14 2015

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

%K nonn

%O 1,3

%A _Patrick De Geest_, Oct 15 2000

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