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

1,2

Links

Table of n, a(n) for n=1..81.

Formula

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

Example

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).

Mathematica

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

Crossrefs

Row lengths are A072047. Rows sums are A319246.

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

Sequence in context: A344090 A344092 A118457 * A343180 A129773 A105789

Adjacent sequences: A319244 A319245 A319246 * A319248 A319249 A319250

Keyword

nonn,tabf

Author

Gus Wiseman, Sep 15 2018

Status

approved