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Search: id:A078651
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| A078651 |
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Number of geometric subsequences of [1,...,n] with integral successive-term ratio and length >= 1. |
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+0
2
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| 1, 3, 5, 9, 11, 15, 17, 23, 27, 31, 33, 40, 42, 46, 50, 59, 61, 68, 70, 77, 81, 85, 87, 97, 101, 105, 111, 118, 120, 128, 130, 141, 145, 149, 153, 165, 167, 171, 175, 185, 187, 195, 197, 204, 211, 215, 217, 231, 235, 242, 246, 253, 255, 265, 269, 279, 283, 287
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The number of geometric subsequences of [1,...,n] with integral successive-term ratio r and length k is floor(n/r^(k-1))(n > 0, r > 1, k > 0).
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FORMULA
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a(n) = n + sum {r > 1, j > 0} floor(n/r^j)
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EXAMPLE
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a(1): [1]; a(2): [1],[2],[1,2]; a(3): [1],[2],[3],[1,2],[1,3]
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CROSSREFS
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a(n) = n + A078632(n).
Sequence in context: A084060 A024896 A040976 this_sequence A101114 A120696 A071156
Adjacent sequences: A078648 A078649 A078650 this_sequence A078652 A078653 A078654
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KEYWORD
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nonn,easy
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AUTHOR
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Robert E. Sawyer (rs.1(AT)mindspring.com), Jan 08, 2003
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