Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
reviewed
approved
proposed
reviewed
editing
proposed
(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
proposed
editing
editing
proposed
editing
proposed
The largest LCM is attained for a partition of n into powers of distinct odd primes and 1s1's.
proposed
editing
editing
proposed
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, 85085, 85085, 109395, 255255, 255255, 285285, 285285, 285285, 285285, 765765, 765765, 855855, 855855, 855855, 855855, 1119195, 1119195, 1322685, 1322685, 1616615, 1616615, 2078505, 4849845, 4849845, 4849845, 4849845, 5870865, 5870865, 14549535, 14549535, 14549535, 14549535, 17612595, 17612595, 19684665, 19684665, 19684665, 19684665, 25741485, 25741485, 30421755, 30421755, 37182145, 37182145, 47805615, 111546435, 111546435, 111546435, 111546435, 111546435, 111546435, 334639305, 334639305, 334639305, 334639305, 334639305, 334639305, 421936515, 421936515, 451035585, 451035585, 510765255, 510765255, 570855285, 570855285, 610224615, 610224615, 746503065, 746503065, 1003917915, 1003917915, 1673196525, 1673196525, 1673196525, 3234846615, 3234846615, 3457939485, 3457939485, 3457939485, 3457939485, 9704539845, 9704539845, 10373818455, 10373818455, 10373818455, 10373818455, 10373818455, 10373818455
Petr Gregor, Arturo Merino, and Torsten Mütze, <a href="https://arxiv.org/abs/2205.08126">The Hamilton compression of highly symmetric graphs</a>, arXiv preprint arXiv:2205.08126 [math.CO], 2022.