A363676 Numbers k such that the least common multiple of the degrees of the irreducible characters of A_k equals |A_k| = k!/2.

0, 1, 2, 5, 6, 8, 10, 12, 17, 21, 30, 36, 57, 66, 80, 105, 120, 122, 136, 190, 192, 210, 212, 233, 276, 302, 325, 380, 408, 465, 496, 530, 561, 597, 630, 632, 666, 705, 741, 780, 782, 822, 905, 990, 992, 1081, 1130, 1176, 1225, 1433, 1540, 1542, 1596, 1772

Offset

1,3

Comments

Intersection of the sequences of numbers k such that there exists a 2-core partition of k or k-2 and a 3-core partition of k. This sequence contains A363675.

Links

Table of n, a(n) for n=1..54.

Diego Martin Duro, Arithmetic Properties of Character Degrees and the Generalised Knutson Index, arXiv:2306.12408 [math.RT], 2023.

Example

The degrees of the irreducible characters of A_5 are 1,3,3,4,5 so their least common multiple is 5!/2 = 60, so 5 is a term of the sequence.

Crossrefs

Cf. A000217, A010054, A175595, A260682, A267137, A363675, A363701.

Sequence in context: A187476 A121411 A224889 * A047441 A284777 A344312

Adjacent sequences: A363673 A363674 A363675 * A363677 A363678 A363679

Keyword

nonn

Author

Diego Martin Duro, Jun 14 2023

Extensions

More terms from Alois P. Heinz, Jun 16 2023

Status

approved