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A296150 Triangle whose n-th row is the integer partition with Heinz number n. 150


%S 1,2,1,1,3,2,1,4,1,1,1,2,2,3,1,5,2,1,1,6,4,1,3,2,1,1,1,1,7,2,2,1,8,3,

%T 1,1,4,2,5,1,9,2,1,1,1,3,3,6,1,2,2,2,4,1,1,10,3,2,1,11,1,1,1,1,1,5,2,

%U 7,1,4,3,2,2,1,1,12,8,1,6,2,3,1,1,1,13,4

%N Triangle whose n-th row is the integer partition with Heinz number n.

%C Same as A112798 with rows reversed. Row lengths are A001222. Rows sums are A056239.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%H Robert Israel, <a href="/A296150/b296150.txt">Table of n, a(n) for n = 1..10002</a> (rows 1 to 3272, flattened)

%e Sequence of partitions begins: (), (1), (2), (11), (3), (21), (4), (111), (22), (31), (5), (211), (6), (41), (32), (1111), (7), (221).

%p f := n -> op(map(numtheory:-pi, sort(map(`$`@op, ifactors(n)[2]), `>`))):

%p map(f, [$1..100]); # _Robert Israel_, Feb 09 2018

%t Table[If[n===1,{},Join@@Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]],{n,50}]

%Y Cf. A000041, A000720, A001222, A056239, A063834, A112798, A196545, A215366, A289501, A299200, A299201, A299202, A299203.

%K nonn,tabf,look

%O 1,2

%A _Gus Wiseman_, Feb 05 2018

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)