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).

1, 1, 3, 2, 1, 2, 7, 1, 1, 2, 3

Offset: 1

Author

Bernard Schott, Dec 05 2021

Keywords

• nonn
• more

Comments

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.

All terms up to a(11) come from Curran's link.

Examples

			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.
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.
		

Links

• M. J. Curran, Non-CLT groups of small order, Comm. Algebra 11 (1983), 111-126.
• Des MacHale and J. Manning, Converse Lagrange Theorem Orders and Supersolvable Orders, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.
• Index entries for sequences related to groups.

Crossrefs

Cf. A000001, A340511, A341048.