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A349930 a(n) is the number of groups of order A340511(n) which have no subgroup of order d, for some divisor d of A340511(n).

%I A349930 #11 Dec 09 2021 21:20:10
%S A349930 1,1,3,2,1,2,7,1,1,2,3
%N A349930 a(n) is the number of groups of order A340511(n) which have no subgroup of order d, for some divisor d of A340511(n).
%C A349930 Also, number of NCLT groups of order A340511(n); NCLT means "Non-Converse Lagrange Theorem" because the converse to Lagrange's theorem does not hold for the groups of this sequence.
%C A349930 All terms up to a(11) come from Curran's link.
%H A349930 M. J. Curran, <a href="https://doi.org/10.1080/00927878308822841">Non-CLT groups of small order</a>, Comm. Algebra 11 (1983), 111-126.
%H A349930 Des MacHale and J. Manning, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Manning/manning5.html">Converse Lagrange Theorem Orders and Supersolvable Orders</a>, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.
%H A349930 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>.
%e A349930 A340511(1) = 12, and there is only one group of order 12: Alt(4) = A_4 which has no subgroup of order d = 6, despite the fact that 6 divides 12, hence a(1) = 1.
%e A349930 A340511(3) = 36, and there are 3 such NCLT groups of order 36: one group (C_3)^2 X C_4 has no subgroup of order 12, and the two groups A_4 X C_3 and (C_2)^2 X C_9 have no subgroup of order 18, hence a(3) = 3.
%Y A349930 Cf. A000001, A340511, A341048.
%K A349930 nonn,more
%O A349930 1,3
%A A349930 _Bernard Schott_, Dec 05 2021