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A181189 Maximal number of elements needed to identify an abelian group of order n by testing the order of random elements. 1
0, 0, 3, 0, 0, 0, 5, 4, 0, 0, 7, 0, 0, 0, 9, 0, 7, 0, 11, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..23.

FORMULA

For all squarefree n, a(n)=0, since there is only one abelian group of order n. Hence the group is trivially known without any checking.

EXAMPLE

For n=20, by the fundamental theorem of finite abelian groups, the group is either Z20 or Z10 x Z2. At worst, you could choose the identity, 1 element of order 2, 4 elements of order 5, and 4 elements of order 10. Then you still wouldn't know which group you have. But the order of the next element you choose will determine the group you have. So a(20)=11.

CROSSREFS

Cf. A005117.

Sequence in context: A330734 A081805 A333784 * A327889 A221702 A084681

Adjacent sequences: A181186 A181187 A181188 * A181190 A181191 A181192

KEYWORD

more,nonn

AUTHOR

Isaac Lambert, Oct 10 2010

STATUS

approved

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Last modified November 27 13:09 EST 2022. Contains 358405 sequences. (Running on oeis4.)