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 A298739 First differences of A000001 (the number of groups of order n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..2046 H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644. Gordon Royle, Numbers of Small Groups FORMULA a(n) = A000001(n+1) - A000001(n). EXAMPLE 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. MAPLE with(GroupTheory): seq((NumGroups(n+1) - NumGroups(n), n=1..500)); PROG (GAP) List([1..700], n -> NumberSmallGroups(n+1) - NumberSmallGroups(n)); CROSSREFS Cf. A000001 (Number of groups of order n). Sequence in context: A106646 A056969 A131106 * A325011 A294188 A331956 Adjacent sequences:  A298736 A298737 A298738 * A298740 A298741 A298742 KEYWORD sign AUTHOR Muniru A Asiru, Jan 25 2018 STATUS approved

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Last modified March 29 15:16 EDT 2020. Contains 333107 sequences. (Running on oeis4.)