A317508 - OEIS

A317508

Number of ways to split the integer partition with Heinz number n into consecutive subsequences with weakly decreasing sums.

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 5, 1, 3, 1, 4, 2, 2, 1, 6, 2, 2, 3, 4, 1, 4, 1, 7, 2, 2, 2, 6, 1, 2, 2, 7, 1, 4, 1, 4, 3, 2, 1, 10, 2, 3, 2, 4, 1, 5, 2, 7, 2, 2, 1, 7, 1, 2, 4, 11, 2, 4, 1, 4, 2, 4, 1, 9, 1, 2, 3, 4, 2, 4, 1, 11, 5, 2, 1, 8, 2, 2

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OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

The a(60) = 7 split partitions:

(3)(2)(1)(1)

(32)(1)(1)

(3)(21)(1)

(3)(2)(11)

(321)(1)

(32)(11)

(3211)

MATHEMATICA

comps[q_]:=Table[Table[Take[q, {Total[Take[c, i-1]]+1, Total[Take[c, i]]}], {i, Length[c]}], {c, Join@@Permutations/@IntegerPartitions[Length[q]]}];

Table[Length[Select[compositionPartitions[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]], OrderedQ[Total/@#]&]], {n, 100}]

CROSSREFS

Cf. A001970, A056239, A063834, A255397, A296150, A316223, A317545, A317546, A319002, A319004.

Cf. A316245, A317715, A318434, A318683, A318684, A319794.

Sequence in context: A034836 A316365 A292886 * A323438 A317141 A317791

Adjacent sequences: A317505 A317506 A317507 * A317509 A317510 A317511

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 29 2018

STATUS

approved