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A132188
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Number of 3-term geometric progressions with no term exceeding n.
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1
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1, 2, 3, 6, 7, 8, 9, 12, 17, 18, 19, 22, 23, 24, 25, 32
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the number of 2 X 2 symmetric singular matrices with entries from {1, ..., n} - cf. A064368.
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REFERENCES
| Gerry Myerson, Trifectas in Geometric Progression, Australian Mathematical Society Gazette, 2008, to appear.
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FORMULA
| a(n) = Sum [sqrt(n/k)]^2, where the sum is over all squarefree k not exceeding n.
If we call A120486, this sequence and A132189 F(n), P(n) and S(n), respectively, then P(n) = 2 F(n) - n = S(n) + n. The Finch-Sebah paper cited at A000188 proves that F(n) is asymptotic to (3 / pi^2) n log n. In the reference, we prove that F(n) = (3 / pi^2) n log n + O(n), from which it follows that P(n) = (6 / pi^2) n log n + O(n) and similarly for S(n).
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CROSSREFS
| Sequence in context: A161824 A102806 A003605 * A060132 A059590 A144705
Adjacent sequences: A132185 A132186 A132187 * A132189 A132190 A132191
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KEYWORD
| nonn,more
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AUTHOR
| Gerry Myerson (gerry(AT)ics.mq.edu.au), Nov 21 2007
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