1,1,0,0,+1,0,+1,0,0,0,0,1,......
Antreas P. Hatzipolakis
xpolakis at otenet.gr
Tue May 23 21:26:46 CEST 2000
Let c_r be defined for r = 1,2,...., by
c_r = 0, if r is not of the form m(3m+1)/2,
c_r = (1)^m, if r is of the form m(3m+1)/2,
Thus,
r  1 2 3 4 5 6 7 8 9 10 11 12

c_r  1, 1, 0, 0, +1, 0, +1, 0, 0, 0, 0, 1
Show that the sum of the kth powers of the roots of
x^n + c_1x^(n1) + c_2x^(n2) + .... + c_(n1)x + c_n = 0
(for k = 1,2,...,n) is s_k = the sum of the divisprs of k (independent of n).
Thus,
k  1 2 3 4 5 6 7 8 9 10 11 12 ...

s_r  1 3 4 7 6 12 8 15 13 18 12 28 ....
The American Mathematical Monthly 39 (1932), p. 300, #3553 by A. A. Bennett
Antreas
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