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A335000
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Orders of the groups PSL(m,q) in increasing order as q runs through the prime powers (with repetitions).
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4
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6, 12, 60, 60, 168, 168, 360, 504, 660, 1092, 2448, 3420, 4080, 5616, 6072, 7800, 9828, 12180, 14880, 20160, 20160, 25308, 32736, 34440, 39732, 51888, 58800, 74412, 102660, 113460, 150348, 178920, 194472, 246480, 262080, 265680, 285852, 352440, 372000, 456288, 515100, 546312
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OFFSET
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1,1
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COMMENTS
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60 is the order of PSL(2,4) and of PSL(2,5).
168 is the order of PSL(2,7) and of PSL(3,2).
20160 is the order of PSL(4,2) and of PSL(3,4).
Other repetitions > 20160 for PSL(m,q) groups are not known.
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LINKS
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FORMULA
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#PSL(m,q) = (Product_{j=0..m-2} (q^m - q^j)) * q^(m-1) / gcd(m,q-1). - Bernard Schott, May 19 2020
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EXAMPLE
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a(5) = #PSL(2,7) = (7^2-1)*7/gcd(2,6) = 168, and,
a(6) = #PSL(3,2) = (2^3-1)*(2^3-2)*2^2/gcd(3,1) = 168.
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CROSSREFS
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Cf. A334884 (another case with repetitions), A334994 (without repetitions).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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