A120253 Number of subsets of integers in the interval [n^2+1, (n+1)^2-1] whose product is twice a square.

1, 1, 1, 1, 2, 1, 2, 4, 2, 4, 4, 4, 8, 4, 32, 8, 16, 16, 32, 16, 32, 128, 32, 64, 64, 128, 512, 32, 512, 128, 256, 2048, 256, 2048, 256, 1024, 512, 8192, 4096, 1024, 4096, 4096, 8192, 16384, 4096, 32768, 32768, 4096, 131072, 16384, 131072, 16384, 524288

Offset

1,5

Comments

Also the number of subsets in the same interval whose product is precisely a square, if 1 is included.

Links

Table of n, a(n) for n=1..53.

Andrew Granville and John Selfridge, Product of integers in an interval, modulo squares, Electronic Journal of Combinatorics, Volume 8(1), 2001.

Formula

a(n) = 2^A120254(n).

Example

a(5) = 2 because the interval [26,35] contains two sets of such integers: {32} and {27,28,30,35}.

Crossrefs

Cf. A120254. A099500 is the number of distinct products which are twice a square. A099501 is the smallest size of a subset which is twice a square.

Sequence in context: A324382 A234359 A099500 * A307018 A274624 A263050

Adjacent sequences: A120250 A120251 A120252 * A120254 A120255 A120256

Keyword

nonn

Author

Martin Fuller, Jun 13 2006

Status

approved