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A298739
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First differences of A000001 (the number of groups of order n).
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1
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0, 0, 1, -1, 1, -1, 4, -3, 0, -1, 4, -4, 1, -1, 13, -13, 4, -4, 4, -3, 0, -1, 14, -13, 0, 3, -1, -3, 3, -3, 50, -50, 1, -1, 13, -13, 1, 0, 12, -13, 5, -5, 3, -2, 0, -1, 51, -50, 3, -4, 4, -4, 14, -13, 11, -11, 0, -1, 12, -12, 1, 2, 263, -266, 3, -3
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OFFSET
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1,7
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LINKS
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FORMULA
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EXAMPLE
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There is only one group of order 1 and of order 2, so a(1) = A000001(2) - A000001(1) = 1 - 1 = 0.
There are 2 groups of order 4 and 3 is a cyclic number, so a(3) = A000001(4) - A000001(3) = 2 - 1 = 1.
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MAPLE
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with(GroupTheory): seq((NumGroups(n+1) - NumGroups(n), n=1..500));
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MATHEMATICA
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(* Please note that, as of version 14, the Mathematica function FiniteGroupCount returns a wrong value for n = 1024 (49487365422 instead of 49487367289). *)
Differences[FiniteGroupCount[Range[100]]] (* Paolo Xausa, Mar 22 2024 *)
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PROG
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(GAP) List([1..700], n -> NumberSmallGroups(n+1) - NumberSmallGroups(n));
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CROSSREFS
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Cf. A000001 (Number of groups of order n).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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