A397045 Number of distinct values in the interval [n,n+1) that can be represented as a sum of square roots of positive integers.

3, 7, 17, 35, 76, 148, 295, 564, 1068, 1965, 3579, 6397, 11318, 19774, 34156, 58444, 99050, 166319, 277066, 458000, 751610, 1224935, 1983456, 3191878, 5106583, 8124040, 12856700, 20243194, 31718970, 49469766, 76809925, 118750958, 182838429, 280394529, 428363342

Offset

1,1

Comments

Number of distinct values in the interval [0,n+1) that can be represented as a sum of square roots of integers (or equivalently, squarefree integers) k > 1. - Charles R Greathouse IV, Jun 15 2026

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..75

Formula

Conjecture: log a(n) ~ k*n^(2/3). Possibly k = (81*zeta(3)/Pi^2)^(1/3) = 2.1447.... - Charles R Greathouse IV, Jun 15 2026

Example

For n=1, the interval is [1,2). The representable values are 1, sqrt(2), and sqrt(3). So a(1) = 3.
For n=2, the interval is [2,3). The representable values are 2, 1+sqrt(2), 1+sqrt(3), sqrt(5), sqrt(6), sqrt(7), and sqrt(8). So, a(2) = 7.

Crossrefs

Sequence in context: A034482 A114100 A260677 * A014395 A326520 A390208

Adjacent sequences: A397042 A397043 A397044 * A397046 A397047 A397048

Keyword

nonn

Author

Ali Sada, Jun 14 2026

Extensions

a(11)-a(13) from Stefano Spezia, Jun 14 2026

a(14)-a(35) from Charles R Greathouse IV, Jun 14 2026

Status

approved