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

1,3

Comments

The largest LCM is attained for a partition of n into powers of distinct odd primes and 1's.

Links

Table of n, a(n) for n=1..52.

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

Example

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.

Prog

(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

Crossrefs

Cf. A000793, A051593, A355573, A159685.

Sequence in context: A339101 A142456 A098508 * A051593 A142712 A247577

Adjacent sequences: A355569 A355570 A355571 * A355573 A355574 A355575

Keyword

nonn

Author

Torsten Muetze, Jul 07 2022

Status

approved