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A300351 Triangle whose n-th row lists in order all Heinz numbers of integer partitions of n into odd parts.

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%I A300351 #5 Mar 03 2018 22:07:16
%S A300351 1,2,4,5,8,10,16,11,20,32,22,25,40,64,17,44,50,80,128,34,55,88,100,
%T A300351 160,256,23,68,110,125,176,200,320,512,46,85,121,136,220,250,352,400,
%U A300351 640,1024,31,92,170,242,272,275,440,500,704,800,1280,2048,62,115,184
%N A300351 Triangle whose n-th row lists in order all Heinz numbers of integer partitions of n into odd parts.
%C A300351 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A300351 Triangle of partitions into odd parts begins:
%e A300351                    0
%e A300351                   (1)
%e A300351                   (11)
%e A300351                 (3) (111)
%e A300351                (31) (1111)
%e A300351             (5) (311) (11111)
%e A300351         (51) (33) (3111) (111111)
%e A300351     (7) (511) (331) (31111) (1111111)
%e A300351 (71) (53) (5111) (3311) (311111) (11111111)
%t A300351 Table[Sort[Times@@Prime/@#&/@Select[IntegerPartitions[n],And@@OddQ/@#&]],{n,0,12}]
%Y A300351 Cf. A000009, A031368, A056239, A066208, A078408, A215366, A246867, A299759, A299757, A300063, A300272.
%K A300351 nonn,tabf
%O A300351 1,2
%A A300351 _Gus Wiseman_, Mar 03 2018