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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

Index entries for sequences related to 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.)