%I #61 Oct 18 2023 09:08:06

%S 0,1,6,10,21,36,66,105,120,136,190,210,276,325,465,496,561,630,666,

%T 741,780,990,1081,1176,1225,1540,1596,1830,2080,2145,2346,2556,2926,

%U 3081,3160,3240,3486,3570,3916,4005,4186,4560,4656,4950,5050,5356,5460,5886,6105

%N Numbers k such that the least common multiple of the degrees of the irreducible characters of S_k equals |S_k| = k!.

%C Intersection of the sequences of numbers k such that there exists a 2-core partition of k (A267137) and a 3-core partition of k (A000217).

%H Alois P. Heinz, <a href="/A363675/b363675.txt">Table of n, a(n) for n = 1..100</a>

%H Diego Martin Duro, <a href="https://arxiv.org/abs/2306.12408">Arithmetic Properties of Character Degrees and the Generalised Knutson Index</a>, arXiv:2306.12408 [math.RT], 2023.

%F From _Alois P. Heinz_, Jun 16 2023: (Start)

%F { k : A175595(k,2) > 0 and A175595(k,3) > 0 }.

%F { k : A010054(k) > 0 and A033687(k) > 0 }. (End)

%Y Cf. A000142, A000217, A010054, A033687, A175595, A260682, A267137, A363676, A363701.

%K nonn

%O 1,3

%A _Diego Martin Duro_, Jun 14 2023

%E More terms from _Alois P. Heinz_, Jun 16 2023