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Search: id:A136185
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| A136185 |
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Number of metacyclic groups of order p^n, prime p >= 3. |
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2
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| 1, 2, 3, 5, 7, 11, 14, 20, 25, 33, 40, 51, 60, 74, 86, 103, 118, 139, 157, 182, 204, 233, 259, 293, 323, 362, 397, 441, 481, 531, 576, 632, 683, 745, 802, 871, 934, 1010, 1080, 1163, 1240, 1331, 1415, 1514, 1606, 1713, 1813, 1929, 2037, 2162, 2279, 2413, 2539
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For number of metacyclic groups of order 2^n see A136184.
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..1000 [Values computed with MAGMA]
MAGMA Computational Algebra System, V2.14-1, Metacyclic p-groups
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FORMULA
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G.f. (conjectured): -x*(x^7 - 2*x^5 + x^3 + x^2 - x - 1)/((x - 1)^4*(x + 1)^2*(x^2 + x + 1)).
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EXAMPLE
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a(4) = 5 since there are five metacyclic groups of order p^4; they have invariants <4, 0, 0, 4, [ p^4 ], >, <1, 2, 1, 2, [], >, <1, 2, 2, 2, [], >, <2, 2, 2, 2, [], > and <1, 3, 1, 1, [], > resp. (for details see MAGMA link).
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PROGRAM
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(MAGMA) [ NumberOfMetacyclicPGroups(3, n): n in [1..53] ];
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CROSSREFS
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Cf. A136184.
Sequence in context: A029982 A070026 A036608 this_sequence A026812 A001402 A008629
Adjacent sequences: A136182 A136183 A136184 this_sequence A136186 A136187 A136188
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 19 2007
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