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

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

Offset

1,2

Comments

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

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

Links

Robert Israel, Table of n, a(n) for n = 1..10002 (rows 1 to 3272, flattened)

Example

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

Maple

f := n -> op(map(numtheory:-pi, sort(map(`$`@op, ifactors(n)[2]), `>`))):
map(f, [$1..100]); # Robert Israel, Feb 09 2018

Mathematica

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

Crossrefs

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

Sequence in context: A025831 A184751 A355534 * A079673 A124829 A093394

Adjacent sequences: A296147 A296148 A296149 * A296151 A296152 A296153

Keyword

nonn,tabf,look

Author

Gus Wiseman, Feb 05 2018

Status

approved