Permutations Of Relative-Primality
Leroy Quet
qqquet at mindspring.com
Fri Nov 1 02:52:39 CET 2002
Just posted this to sci.math:
Let {a(k)} be a permutation of {1,2,3,...,n}.
How many permutions of 1-through-n are there such that
GCD( sum{k=1 to m} a(k) , a(m+1) ) = 1
for all positive integers m <= n-1 ?
The sequence begins: 1, 2, 2, 8,.... (*)
(This sequence is too short to do an easy search on the EIS.)
Two things:
For n >= 2, a(1) can be exchanged with a(2), so the n'th term of the
sequence (*) is even.
Also, a(n) must be relatively prime with n(n+1)/2.
Thanks,
Leroy Quet
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