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A349930
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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).
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0
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1, 1, 3, 2, 1, 2, 7, 1, 1, 2, 3
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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