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.

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.

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

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

Cf. A006255, A066400, A072905.

Sequence in context: A228483 A129979 A274709 * A365711 A237347 A075017

Adjacent sequences: A260893 A260894 A260895 * A260897 A260898 A260899

Keyword

nonn

Author

Peter Kagey, Aug 03 2015

Status

approved