A110261 Number of distinct numbers that can be written as floor(n/i)+floor(n/j), 1<=i<=j<=n.

1, 3, 3, 6, 6, 9, 9, 10, 12, 13, 13, 16, 16, 17, 17, 20, 20, 21, 21, 24, 24, 25, 25, 26, 28, 29, 29, 30, 30, 33, 33, 34, 34, 35, 34, 38, 38, 39, 39, 40, 40, 43, 43, 44, 45, 44, 44, 45, 48, 48, 50, 50, 50, 51, 51, 54, 55, 54, 54, 55, 55, 56, 57, 60, 60, 61, 61, 62, 62, 61, 61, 65

Offset

1,2

Comments

a(p) = a(p-1) for odd primes p;

the sequence is not monotonically increasing, see A110264 for numbers m with a(m)<a(m-1);

a(m)<a(A110262(n)) for m < A110262(n), a(A110262(n))=A110263(n);

A110265(n) = (smallest number <> floor(n/i)+floor(n/j), 1<=i<=j<=n).

Links

Table of n, a(n) for n=1..72.

Example

a(10) = #{20,15,13,12,11,10,8,7,6,5,4,3,2} = 13:
20=10/1+10/1, 15=10/1+10/2, 13=10/1+[10/3], 12=10/1+10/5,
11=10/1+[10/6], 10=10/2+10/2, 8=10/2+[10/3], 7=10/2+10/5, 6=10/2+[10/6],
5=[10/3]+10/5, 4=10/5+10/5, 3=10/5+[10/6] and 2=[10/6]+[10/6].

Crossrefs

Sequence in context: A165885 A227128 A061795 * A168237 A290966 A049318

Adjacent sequences: A110258 A110259 A110260 * A110262 A110263 A110264

Keyword

nonn

Author

Reinhard Zumkeller, Jul 18 2005

Status

approved