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A260896
a(n) gives the number of integers m such that there exist k and h with 2n^2 < mk^2 < 2(n+1)^2 and 2n^2 < 2mh^2 < 2(n+1)^2.
1
0, 1, 0, 1, 1, 1, 3, 3, 2, 3, 2, 2, 3, 3, 0, 3, 1, 4, 2, 3, 3, 1, 6, 3, 4, 4, 5, 3, 2, 5, 4, 8, 4, 4, 5, 1, 5, 6, 4, 5, 3, 6, 2, 5, 7, 5, 8, 4, 7, 4, 7, 7, 7, 10
OFFSET
0,7
COMMENTS
A072905(2n^2) > A006255(2n^2) and A066400(2n^2) > 2 for all n such that a(n) > 0.
Conjecture: a(n) > 0 for all n > 14.
EXAMPLE
For n=12 the a(12)=3 solutions are 3, 6, and 37:
(1) (a) 2 * 12^2 < 3 * 10^2 < 2 * 13^2
(b) 2 * 12^2 < 2 * 3 * 7^2 < 2 * 13^2
(2) (a) 2 * 12^2 < 6 * 7^2 < 2 * 13^2
(b) 2 * 12^2 < 2 * 6 * 5^2 < 2 * 13^2
(3) (a) 2 * 12^2 < 37 * 3^2 < 2 * 13^2
(b) 2 * 12^2 < 2 * 37 * 2^2 < 2 * 13^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Aug 03 2015
STATUS
approved