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A317508 Number of ways to split the integer partition with Heinz number n into consecutive subsequences with weakly decreasing sums. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 17:05 EDT 2021. Contains 345085 sequences. (Running on oeis4.)