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A355573
Largest LCM of partitions of n with a nonzero even number of even parts.
1
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
4,1
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.
LINKS
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 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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Torsten Muetze, Jul 07 2022
STATUS
approved