A112409 - OEIS

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A112409

Table read by rows: for each n: the orders of the permutations of n elements, excluding those that are a divisor of the order of another permutation of n elements.

1

1, 2, 2, 3, 3, 4, 4, 5, 6, 4, 5, 6, 7, 10, 12, 7, 8, 10, 12, 15, 8, 9, 12, 14, 15, 20, 8, 9, 12, 14, 20, 21, 30, 11, 18, 20, 21, 24, 28, 30, 11, 18, 24, 28, 35, 42, 60, 13, 22, 24, 28, 35, 36, 40, 42, 60, 13, 22, 24, 33, 36, 40, 45, 60, 70, 84, 24, 26, 33, 36, 40, 44, 45, 56, 60, 70, 84, 105

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..2875 (rows 1..50)

EXAMPLE

Triangle begins:

1: 1,

2: 2,

3: 2 3,

4: 3 4,

5: 4 5 6,

6: 4 5 6,

7: 7 10 12,

...

Permutations of 7 elements have orders of 1, 2, 3, 4, 5, 6, 7, 10, 12, of which 7, 10 and 12 are not factors of any others.

PROG

(PARI)

S(n)={my(R=[]); forpart(p=n, R=setunion(R, [lcm(Vec(p))])); R}

row(n)={my(X=S(n)); select(x->1==#select(y->y%x==0, X), X)} \\ Andrew Howroyd, Nov 09 2025

CROSSREFS

Sequence in context: A029030 A008719 A079685 * A256991 A267110 A026261

Adjacent sequences: A112406 A112407 A112408 * A112410 A112411 A112412

KEYWORD

easy,nonn,tabf

AUTHOR

Allen Tracht (atracht(AT)ix.netcom.com), Dec 08 2005

EXTENSIONS

Missing a(16) inserted and a(33) onward from Andrew Howroyd, Nov 09 2025

STATUS

approved