A355573 Largest LCM of partitions of n with a nonzero even number of even parts.

2, 2, 4, 6, 6, 12, 12, 20, 30, 30, 60, 60, 84, 84, 140, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 1540, 2310, 2520, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 27720, 30030, 32760, 60060, 60060, 60060, 60060, 120120, 120120, 180180, 180180, 180180, 180180

Offset: 4

Author

Torsten Muetze, Jul 07 2022

Keywords

• nonn

Comments

The largest LCM is attained for a partition of n into powers of distinct odd primes, 2^k for some k>0, 2, and 1's.

Examples

			The partitions of n=8 with a nonzero even number of even parts are 6+2, 4+4, 4+2+1+1, 3+2+2+1, 2+2+2+2, 2+2+1+1+1+1, and the partition with largest LCM among those is 3+2+2+1, which has LCM(3,2,2,1)=3*2=6, so a(8)=6.
		

Links

• Petr Gregor, Arturo Merino, and Torsten Mütze, The Hamilton compression of highly symmetric graphs, arXiv preprint arXiv:2205.08126 [math.CO], 2022.

Crossrefs

Cf. A000793, A051593, A355572, A159685.