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A350159
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Number of subgroups of the dicyclic group Dic_n.
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0
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3, 6, 8, 11, 10, 18, 12, 20, 19, 24, 16, 36, 18, 30, 32, 37, 22, 48, 24, 50, 40, 42, 28, 70, 37, 48, 48, 64, 34, 84, 36, 70, 56, 60, 56, 103, 42, 66, 64, 100, 46, 108, 48, 92, 90, 78, 52, 136, 63, 102, 80, 106, 58, 132, 80, 130, 88, 96, 64, 184, 66, 102, 116
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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Given the fact that Dic_2 is isomorphic to the quaternion group Q_8, the subgroups of Dic_2 are isomorphic to the subgroups of Q_8 which are {1}, {1,-1}, {1,i,-1,-i}, {1,j,-1,-j}, {1,k,-1,-k} and Q_8.
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MATHEMATICA
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a[n_] := DivisorSigma[0, 2*n] + DivisorSigma[1, n]; Array[a, 50] (* Amiram Eldar, Dec 17 2021 *)
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PROG
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(PARI) a(n) = numdiv(2*n) + sigma(n); \\ Michel Marcus, Dec 18 2021
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CROSSREFS
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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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