m|n => a(m)|a(n)
Christopher Hanusa
chanusa at math.washington.edu
Tue Apr 12 02:26:05 CEST 2005
Hello Seqfans,
I've just come upon a sequence that satisfies the condition "if m
divides n then a(m) divides a(n)". (It's related to the number of domino
tilings of some sequence of regions.)
Two other sequences that satisfy this property are
0) a(n)=n (trivially)
1) Fibonacci indexed where f(1)=f(2)=1
Is there anything known about such sequences in general? or maybe
not-so-much-in-general? I realize that there are infinitely many
sequences that satisfy this --- values for a(p) for p prime are free, and
a(p^i q^j)=k*lcm(a(p^i q^{j-1}),a(p^{i-1} q^j)), where k is free, etc. But
maybe there is some theory around that can help me learn more. How might
one go about finding a closed form? Can you think of any other examples?
What do you think of when you think of this property?
Thanks for any insights,
--Chris
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