cp's OEIS Frontend

A205645 Number of nilpotent loops of order 2*prime(n) up to isotopism.

%I A205645 #16 May 06 2025 10:53:16
%S A205645 3,64,3658004,1023090941561683953759580,
%T A205645 2684673506279593406254437209960379084,
%U A205645 382103603974564085117495134243710834769544696954218618882023686506660
%N A205645 Number of nilpotent loops of order 2*prime(n) up to isotopism.
%C A205645 Table 5, p. 20, of Clavier. oddprime(n) = A065091(n) = A000040(n-1).
%C A205645 In version 2 of Clavier's preprint as well as in the published paper, the numbers have been replaced by numbers 1 smaller: 2, 63, 3658003... Theorem 6.10, which gives a formula, has also been changed. The arXiv source files include a file with all terms for which prime(n) < 100. That file agrees with this sequence rather than with the sequence in the updated version of the preprint (or in the published paper). - _Andrei Zabolotskii_, May 06 2025
%D A205645 L. Clavier, About the autotopisms of abelian groups, 2012.
%D A205645 D. Daly and P. Vojtěchovský, Enumeration of nilpotent loops via cohomology, J. Algebra, 322(11):4080-4098, 2009.
%D A205645 H.O. Pflugfelder, Quasigroups and Loops: Introduction, 1990.
%D A205645 J. D. Phillips and P. Vojtěchovský, The varieties of loops of bolmoufang type, Algebra Universalis, 54(3):259-271, 2005.
%H A205645 Lucien Clavier, <a href="http://arxiv.org/abs/1201.5659">Enumeration of nilpotent loops up to isotopy</a>, arXiv:1201.5659v1 [math.GR], Jan 26, 2012.
%H A205645 Lucien Clavier, <a href="https://dml.cz//handle/10338.dmlcz/142881">Enumeration of nilpotent loops up to isotopy</a>, Commentationes Mathematicae Universitatis Carolinae, 53 (2012), 159-177.
%e A205645 a(4) = 3658004 because prime(4) = 7 and there are 3658004 nilpotent loops of order 2*7 = 14.
%Y A205645 Cf. A000040, A057771, A065091.
%K A205645 nonn
%O A205645 2,1
%A A205645 _Jonathan Vos Post_, Jan 29 2012