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A319247
Irregular triangle whose n-th row lists the strict integer partition whose Heinz number is the n-th squarefree number.
12
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
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.
Sequence in context: A344090 A344092 A118457 * A343180 A129773 A105789
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Sep 15 2018
STATUS
approved