cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A060702 Orders of finite groups that have trivial center.

Original entry on oeis.org

1, 6, 10, 12, 14, 18, 20, 21, 22, 24, 26, 30, 34, 36, 38, 39, 42, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 66, 68, 70, 72, 74, 75, 78, 80, 82, 84, 86, 90, 93, 94, 96, 98, 100, 102, 106, 108, 110, 111, 114, 116, 118, 120, 122, 126, 129, 130, 132, 134, 136
Offset: 1

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Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 20 2001

Keywords

Comments

Apart from the first element 1 this is a subsequence of A056868 because a nilpotent group has nontrivial center. If n = 0 mod 6 or n >= 6 and n = 2 mod 4 then n is in this sequence.
If n >= 6 and n == 2 mod 4 then n is a member of the sequence because of the dihedral group of order 2(2k+1). In addition, if p is a prime and p == 1 mod 4 then n=4p is a member of the sequence; however, if p == 3 mod 4 and p>5, then n=4p is not a member of the sequence. Furthermore, if n=pq where p and q are distinct odd primes with pDes MacHale and Mossie Crowe, Jul 05 2005
This sequence is closed under multiplication. - Eric M. Schmidt, Aug 27 2012

Examples

			The symmetric group S_3 of order 6 has trivial center so 6 belongs to the sequence.

Links

Crossrefs

Cf. A056868, A059806.
For the corresponding numbers of centerless groups of these orders see A357900.

Extensions

The old entry 89 was an error, since it is a prime. - Robert F. Bailey (robertb(AT)math.carleton.ca) and Brett Stevens (brett(AT)math.carleton.ca), Jul 16 2009
Sequence extended and corrected by Eric M. Schmidt, Aug 27 2012

A357924 Number of groups of order n with trivial center.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 5, 1, 1, 1, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 6, 0, 1, 1, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 5, 0, 2, 0, 5
Offset: 1

Views

Author

Jianing Song, Oct 20 2022

Keywords

Comments

A357900 is the main sequence.

Crossrefs

Cf. A357900, A060702 (indices of terms > 0).
Showing 1-2 of 2 results.

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