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%I #15 Feb 20 2020 13:56:03
%S 2,6,4,30,8,210,36,16,2310,32,30030,900,216,64,510510,128,9699690,
%T 44100,1296,256,223092870,27000,512,6469693230,5336100,7776,1024,
%U 200560490130,2048,7420738134810,901800900,9261000,810000,46656,4096,304250263527210,8192
%N 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.
%C 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).
%e Triangle begins:
%e 2
%e 6 4
%e 30 8
%e 210 36 16
%e 2310 32
%e 30030 900 216 64
%e 510510 128
%e 9699690 44100 1296 256
%e 223092870 27000 512
%e 6469693230 5336100 7776 1024
%e Corresponding triangle of integer partitions whose Heinz numbers belong to the triangle begins:
%e (1)
%e (21) (11)
%e (321) (111)
%e (4321) (2211) (1111)
%e (54321) (11111)
%e (654321) (332211) (222111) (111111)
%e (7654321) (1111111)
%e (87654321) (44332211) (22221111) (11111111)
%e (987654321) (333222111) (111111111)
%t Table[Product[Prime[i]^d,{i,n/d}],{n,12},{d,Divisors[n]}]
%Y First column is A002110.
%Y Cf. A000961, A001597, A002110, A007947, A025487, A047966, A055932, A056239, A072774, A100778, A304250, A322793.
%K nonn,tabf
%O 1,1
%A _Gus Wiseman_, Dec 26 2018
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