A145266 A positive integer n is included if there does not exist a positive integer m such that Sum{k>=0} floor(n/(m+k)) = n.

2, 3, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 20, 21, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 38, 39, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 56, 57, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 74, 75, 78, 79, 81, 82, 83, 84, 85, 86, 88, 89, 92, 93, 96, 97, 99, 100, 101, 102, 103, 104

Offset

1,1

Comments

This sequence is the complement of sequence A145265. A145264(a(n)) = 0.

Does this sequence contain all of those and only those, positive integers that are congruent to 2, 3, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17 (mod 18)? - Leroy Quet, Oct 31 2008

Links

Table of n, a(n) for n=1..70.

Example

Checking n = 8: floor(8/3) + floor(8/4) + floor(8/5) + floor(8/6) + floor(8/7) + floor(8/8) = 2 + 2 + 1 + 1 + 1 + 1 = 8. So 8 is not included in the sequence. Checking n = 6: floor(6/2) + floor(6/3) + floor(6/4) + floor(6/5) + floor(6/6) = 3 + 2 + 1 + 1 + 1 = 8, which is > 6. But floor(6/3) + floor(6/4) + floor(6/5) + floor(6/6) = 2 + 1 + 1 + 1 = 5, which is < 6. So 6 is included in the sequence.

Mathematica

a = {}; For[n = 1, n < 200, n++, c = 1; For[m = 1, m < n + 1, m++, If[Sum[Floor[n/(m + k)], {k, 0, n}] == n, c = 0]]; If[c == 1, AppendTo[a, n]]]; a (* Stefan Steinerberger, Oct 17 2008 *)

Crossrefs

Cf. A145264, A145265.

Sequence in context: A110920 A296414 A267590 * A188078 A188094 A047561

Adjacent sequences: A145263 A145264 A145265 * A145267 A145268 A145269

Keyword

nonn

Author

Leroy Quet, Oct 05 2008

Extensions

More terms from Stefan Steinerberger, Oct 17 2008

More terms from Max Alekseyev, Apr 18 2010

Status

approved