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A322792
Irregular triangle read by rows where if d|n then T(n,d) = A002110(n/d)^d, where A002110(k) is the product of the first k primes.
7
2, 6, 4, 30, 8, 210, 36, 16, 2310, 32, 30030, 900, 216, 64, 510510, 128, 9699690, 44100, 1296, 256, 223092870, 27000, 512, 6469693230, 5336100, 7776, 1024, 200560490130, 2048, 7420738134810, 901800900, 9261000, 810000, 46656, 4096, 304250263527210, 8192
OFFSET
1,1
COMMENTS
A reordering of A100778 (powers of primorials), these are the Heinz numbers of uniform integer partitions of length n whose union is an initial interval of positive integers. An integer partition is uniform if all parts appear with the same multiplicity. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Triangle begins:
2
6 4
30 8
210 36 16
2310 32
30030 900 216 64
510510 128
9699690 44100 1296 256
223092870 27000 512
6469693230 5336100 7776 1024
Corresponding triangle of integer partitions whose Heinz numbers belong to the triangle begins:
(1)
(21) (11)
(321) (111)
(4321) (2211) (1111)
(54321) (11111)
(654321) (332211) (222111) (111111)
(7654321) (1111111)
(87654321) (44332211) (22221111) (11111111)
(987654321) (333222111) (111111111)
MATHEMATICA
Table[Product[Prime[i]^d, {i, n/d}], {n, 12}, {d, Divisors[n]}]
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Dec 26 2018
STATUS
approved