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A078632
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Number of geometric subsequences of [1,...,n] with integral successive-term ratio and length > 1.
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1
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0, 1, 2, 5, 6, 9, 10, 15, 18, 21, 22, 28, 29, 32, 35, 43, 44, 50, 51, 57, 60, 63, 64, 73, 76, 79, 84, 90, 91, 98, 99, 109, 112, 115, 118, 129, 130, 133, 136, 145, 146, 153, 154, 160, 166, 169, 170, 183, 186, 192, 195, 201, 202, 211, 214, 223, 226, 229, 230, 242
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OFFSET
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1,3
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COMMENTS
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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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LINKS
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FORMULA
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a(n) = sum {r > 1, j > 0} floor(n/r^j)
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EXAMPLE
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a(2): [1,2]; a(3): [1,2],[1,3]; a(4): [1,2],[1,3],[1,4],[2,4],[1,2,4]
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CROSSREFS
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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)
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STATUS
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approved
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