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Search: id:A083854
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| A083854 |
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Numbers which are squares, twice squares, three times squares, or six times squares: i.e. numbers whose square-free part divides 6. |
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4
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| 0, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 25, 27, 32, 36, 48, 49, 50, 54, 64, 72, 75, 81, 96, 98, 100, 108, 121, 128, 144, 147, 150, 162, 169, 192, 196, 200, 216, 225, 242, 243, 256, 288, 289, 294, 300, 324, 338, 361, 363, 384, 392, 400, 432, 441, 450, 484, 486, 507
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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It is simple to divide equilateral triangles into these numbers of congruent parts: squares by making smaller equilateral triangles; 6*sqaures by diving each small equilateral triangles by its medians into small right-angled triangles; and 2*squares or 3*squares by recombining three or two of these small right-angled triangles.
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FORMULA
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a(n) is bounded below by 0.137918...*n^2 where 0.137918...=3*(3-2*sqrt(2))*(2-sqrt(3)); the error appears to be O(n).
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CROSSREFS
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Cf. A000290, A007913, A001105, A028982, A033428, A033581, A083855.
Adjacent sequences: A083851 A083852 A083853 this_sequence A083855 A083856 A083857
Sequence in context: A067947 A053640 A097755 this_sequence A003586 A114334 A018690
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 06 2003
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