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A332761 Exponents m such that the number of nonnegative k <= n, possessing the property that n + n*k - k is a square, is equal to 2^m. 1
0, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 3, 1, 1, 1, 3, 2, 1, 2, 3, 1, 2, 2, 2, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
COMMENTS
Where records occur gives 0, 1, 9, 25, 121, 841, 9241, ...
LINKS
FORMULA
a(n+2) is the exponent r if 2^r is equal to the number of squares of the form k + k*n - n, 0 <= k <= n.
a(n) = A072273(n-1). - Jinyuan Wang, Feb 25 2020
EXAMPLE
a(0) = 0 because 0 + 0*0 - 0 = 1 = 1^2 and 1 = 2^0.
a(1) = 1 because 1 + 1*0 - 0 = 1 = 1^2, 1 + 1*1 - 1 = 1^2 and 2 = 2^1.
a(9) = 2 because 9 + 9*0 - 0 = 9 = 3^2, 9 + 9*2 - 2 = 25 = 5^2, 9 + 9*8 - 8 = 64 = 8^2, 9 + 9*9 - 9 = 81 = 9^2 and 4 = 2^2.
PROG
(Magma) [[m: m in [0..n] | #[k: k in [0..n] | IsSquare(n+n*k-k)] eq 2^m]: n in [0..100]];
CROSSREFS
Sequence in context: A215975 A071891 A359306 * A046072 A072273 A157230
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(70) corrected by Jinyuan Wang, Feb 25 2020
STATUS
approved

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)