A355572 Largest LCM of partitions of n into odd parts.

1, 1, 3, 3, 5, 5, 7, 15, 15, 21, 21, 35, 35, 45, 105, 105, 105, 105, 165, 165, 315, 315, 385, 385, 495, 1155, 1155, 1365, 1365, 1365, 1365, 3465, 3465, 4095, 4095, 5005, 5005, 6435, 15015, 15015, 15015, 15015, 19635, 19635, 45045, 45045, 45045, 45045, 58905, 58905, 69615, 69615

Offset: 1

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 and 1's.

Examples

			The partitions of n=8 into odd parts are 7+1, 5+3, 5+1+1+1, 3+3+1+1, 3+1+1+1+1+1, 1+1+1+1+1+1+1+1, and the partition with largest LCM among those is 5+3, which has LCM(5,3)=5*3=15, so a(8)=15.
		

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, A355573, A159685.

Programs

PARI

a(n) = my(x=1); forpart(p=n, if (!#select(x->((x%2)==0), Vec(p)), x = max(x, lcm(Vec(p))))); x; \\ Michel Marcus, Jul 08 2022