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A318434
Number of ways to split the integer partition with Heinz number n into consecutive subsequences with equal sums.
9
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1
OFFSET
1,4
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
The a(3072) = 5 constant-sum split partitions:
(21111111111)
(21111)(111111)
(211)(1111)(1111)
(21)(111)(111)(111)
(2)(11)(11)(11)(11)(11)
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[comps[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]], SameQ@@Total/@#&]], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 29 2018
STATUS
approved