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A145266
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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.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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)? [From Leroy Quet Oct 31 2008]
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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.
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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 [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 17 2008]
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CROSSREFS
| A145264, A145265
Sequence in context: A030164 A066646 A110920 * A188078 A188094 A047561
Adjacent sequences: A145263 A145264 A145265 * A145267 A145268 A145269
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 05 2008
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 17 2008
More terms from Max Alekseyev (maxale(AT)gmail.com), Apr 18 2010
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