

A131597


Bigomega of Pisano periods mod n, i.e., number of prime divisors with multiplicity of the period length of Fibonacci residues mod n.


0



0, 1, 3, 2, 3, 4, 4, 3, 4, 4, 2, 4, 3, 5, 4, 4, 4, 4, 3, 4, 4, 3, 5, 4, 4, 4, 5, 5, 2, 5, 3, 5, 4, 4, 5, 4, 3, 3, 4, 4, 4, 5, 4, 3, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 3, 5, 5, 3, 2, 5, 4, 3, 5, 6, 4, 5, 4, 4, 5, 6, 3, 4, 3, 4, 5, 3, 5, 5, 3, 5, 6, 5, 5, 5, 5, 5, 4, 4, 3, 5, 5, 5, 5, 6, 5, 5, 4, 6, 5, 5, 3, 5, 5, 4, 5
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OFFSET

1,3


COMMENTS

The Pisano sequence (A001175) is not known exactly for all n. It is known that Pisano(n) <= 6n, Pisano(10) = 60, etc. (see A001175). In addition, Pisano(m) is even if m>2, and Pisano(m) = m iff m = 24*5^(k1) for some integer k > 1. Bigomega seems an interesting function of Pisano(n).


LINKS

Table of n, a(n) for n=1..105.
Eric Weisstein's World of Mathematics, Pisano period.
Wikipedia, Pisano period.


FORMULA

a(n) = A001222(A001175(n)).


EXAMPLE

F(mod 5) : 0 1 1 2 3 0 3 3 1 4 0 4 4 3 2 0 2 2 4 1 0 1 1 ...
period : 20; bigomega : 3 (since 20=2*2*5).


CROSSREFS

Cf. A000045, A001175, A001222.
Sequence in context: A094365 A272886 A098822 * A077070 A075988 A029150
Adjacent sequences: A131594 A131595 A131596 * A131598 A131599 A131600


KEYWORD

easy,nonn


AUTHOR

Paul Finley (pfinley(AT)touro.edu), Aug 30 2007


STATUS

approved



