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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 (list; graph; refs; listen; history; text; internal format)
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^(k-1) 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

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Last modified May 16 00:49 EDT 2021. Contains 343937 sequences. (Running on oeis4.)