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A120253
Number of subsets of integers in the interval [n^2+1, (n+1)^2-1] whose product is twice a square.
2
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
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
KEYWORD
nonn
AUTHOR
Martin Fuller, Jun 13 2006
STATUS
approved