A368048 a(n) = lcm_{p in Partitions(n)} (Product_{t in p}(t + m)), where m = 2.

1, 3, 36, 540, 6480, 136080, 8164800, 24494400, 293932800, 48498912000, 4073908608000, 158882435712000, 9532946142720000, 28598838428160000, 343186061137920000, 612587119131187200000, 7351045429574246400000, 419009589485732044800000, 276546329060583149568000000

Offset: 0

Author

Peter Luschny, Dec 12 2023

Keywords

• nonn

Comments

With m = 0, the cumulative radical A048803 is computed, and with m = 1 the Hirzebruch numbers A091137. The general array is A368116. Using the terminology introduced in A368116 a(n) = lcm_{p in P_{2}(n)} Prod(p).

Examples

			Let n = 4. The partitions of 4 are [(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)]. Thus a(4) = lcm([6, 5*3, 4*4, 4*3*3, 3*3*3*3]) = 6480.
		

Crossrefs

Cf. A368092, A048803, A091137, A368116.

Programs

SageMath

def a(n): return lcm(product(r + 2 for r in p) for p in Partitions(n))
print([a(n) for n in range(20)])

Formula

a(n) = A368092(n) * 2^(n - n mod 2).