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 A281554 Number of nonassociative right conjugacy closed loops of order n up to isomorphism. 1
 0, 0, 0, 0, 0, 3, 0, 19, 5, 16, 0, 155, 0, 97, 17, 6317, 0, 1901, 0, 8248, 119, 10487, 0, 471995, 119, 151971, 152701 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS For a groupoid Q and x in Q, define the right (left) translation map R_x: Q->Q by yR_x=yx (L_x: Q->Q by yL_x=xy). A loop is a groupoid Q with neutral element 1 in which all translations are bijections in Q. A loop Q is right conjugacy closed if (R_x)^(-1)R_yR_x is a right translation for every x, y in Q. Since any finite loop of order n < 5 is a group, then nonassociative right conjugacy closed loops exist when the order n > 5. In the literature, every nonassociative right conjugacy closed loop of order n can be represented as a union of certain conjugacy classes of a transitive group of degree n. The number of nonassociative right conjugacy closed loops of order n up to isomorphism were summarized in LOOPS version 3.3.0, Computing with quasigroups and loops in GAP (Groups, Algorithm and Programming). LINKS G. P. Nagy and P. Vojtechovsky, Loops version 3.3.0, Computing with quasigroups and loops in GAP, 2016. EXAMPLE a(6)=3 because there are 3 nonassociative right conjugacy closed loops of order 6 and a(8)=19 because there are 19 nonassociative right conjugacy closed loops of order 8. CROSSREFS Cf. A090750, A281319, A281462. Sequence in context: A013579 A151814 A187804 * A320104 A102840 A009353 Adjacent sequences:  A281551 A281552 A281553 * A281555 A281556 A281557 KEYWORD nonn,more AUTHOR Muniru A Asiru, Jan 24 2017 STATUS approved

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)