A327953 a(n) is the number of positive integers k such that some nontrivial multiple of sqrt(k) falls strictly between n and n+1.

0, 1, 1, 3, 4, 5, 6, 8, 8, 9, 10, 12, 14, 15, 16, 17, 17, 20, 21, 20, 22, 28, 23, 27, 29, 31, 28, 32, 35, 30, 38, 38, 39, 41, 35, 43, 43, 46, 46, 44, 49, 49, 52, 52, 54, 59, 52, 56, 57, 64, 60, 61, 66, 62, 63, 69, 67, 73, 70, 70, 75, 76, 75, 78, 78, 79, 85, 82

Offset

1,4

Comments

"Nontrivial multiple" means a multiplier greater than 1.

Number of nontrivial multiples of squares between (exclusive) n^2 and (n+1)^2. - David A. Corneth, Oct 03 2019

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Formula

a(n) = A327952(n) - 2*n.

Example

For n = 6 the a(6) = 5 values of k are
k = 3  with 6 < 4*sqrt(3)  < 7,
k = 5  with 6 < 3*sqrt(5)  < 7,
k = 10 with 6 < 2*sqrt(10) < 7,
k = 11 with 6 < 2*sqrt(11) < 7, and
k = 12 with 6 < 2*sqrt(12) < 7.

Crossrefs

Cf. A261865, A327952.

Sequence in context: A143152 A229109 A096127 * A352025 A112768 A298420

Adjacent sequences: A327950 A327951 A327952 * A327954 A327955 A327956

Keyword

nonn

Author

Peter Kagey, Oct 01 2019

Status

approved