A319247 Irregular triangle whose n-th row lists the strict integer partition whose Heinz number is the n-th squarefree number.

1, 2, 3, 2, 1, 4, 3, 1, 5, 6, 4, 1, 3, 2, 7, 8, 4, 2, 5, 1, 9, 6, 1, 10, 3, 2, 1, 11, 5, 2, 7, 1, 4, 3, 12, 8, 1, 6, 2, 13, 4, 2, 1, 14, 9, 1, 15, 7, 2, 16, 5, 3, 8, 2, 10, 1, 17, 18, 11, 1, 6, 3, 5, 2, 1, 19, 9, 2, 4, 3, 1, 20, 21, 12, 1, 5, 4, 6, 2, 1, 22

Offset: 1

Author

Gus Wiseman, Sep 15 2018

Keywords

• nonn
• tabf

Examples

			The sequence of strict partitions begins: (), (1), (2), (3), (2,1), (4), (3,1), (5), (6), (4,1), (3,2), (7), (8), (4,2), (5,1), (9), (6,1), (10), (3,2,1), (11), (5,2), (7,1), (4,3), (12), (8,1), (6,2), (13), (4,2,1).
		

Crossrefs

Row lengths are A072047. Rows sums are A319246.

Cf. A000009, A000720, A001222, A005117, A056239, A265668, A296150, A299755.

Programs

Mathematica

Table[If[n==1,{},Join@@Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]],{n,Select[Range[100],SquareFreeQ]}]

Formula

T(n,k) = A000720(A265668(n,-k)).