login
Number of nonisomorphic groups with orders indexed by least prime signatures.
0

%I #18 Jul 29 2024 06:17:29

%S 1,1,2,2,5,5,14,15,4,51,14,52,13,267,50,231,47,2328,197,37,1543,12,

%T 177,208,56092,1045,162,20169,41,775,1213,10494213,8681,840,1090235,

%U 186,4725,150,11394,49487367289,583,157877,131,3609,5958,408641062,1005,47937,749,241004

%N Number of nonisomorphic groups with orders indexed by least prime signatures.

%H H. U. Besche, B. Eick and E. A. O'Brien, <a href="https://web.archive.org/web/20161030100727/http://www.icm.tu-bs.de/ag_algebra/software/small/number.html">Number of isomorphism types of finite groups of given order</a> [Wayback Machine link]

%H David Burrell, <a href="https://doi.org/10.1080/00927872.2021.2006680">On the number of groups of order 1024</a>, Communications in Algebra, Vol. 50, No. 6 (2022), pp. 2408-2410.

%F a(n) = A000001(A025487(n)).

%Y Cf. A000001, A025487.

%K nonn

%O 1,3

%A _Lekraj Beedassy_, Oct 14 2004

%E a(40) corrected by _David Burrell_, Jun 07 2022

%E a(48)-a(50) from _Amiram Eldar_, Jul 29 2024