A397045 - OEIS

%I #27 Jun 17 2026 21:38:19

%S 3,7,17,35,76,148,295,564,1068,1965,3579,6397,11318,19774,34156,58444,

%T 99050,166319,277066,458000,751610,1224935,1983456,3191878,5106583,

%U 8124040,12856700,20243194,31718970,49469766,76809925,118750958,182838429,280394529,428363342

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

%C 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

%H Charles R Greathouse IV, <a href="/A397045/b397045.txt">Table of n, a(n) for n = 1..75</a>

%F 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

%e For n=1, the interval is [1,2). The representable values are 1, sqrt(2), and sqrt(3). So a(1) = 3.

%e 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.

%K nonn

%O 1,1

%A _Ali Sada_, Jun 14 2026

%E a(11)-a(13) from _Stefano Spezia_, Jun 14 2026

%E a(14)-a(35) from _Charles R Greathouse IV_, Jun 14 2026