cp's OEIS Frontend

A318434 Number of ways to split the integer partition with Heinz number n into consecutive subsequences with equal sums.

%I A318434 #18 Sep 29 2018 12:57:17
%S A318434 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,
%T A318434 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,
%U A318434 1,2,1,1,1,1,1,1,1,1,1,1,3,1,1,2,1,1,1
%N A318434 Number of ways to split the integer partition with Heinz number n into consecutive subsequences with equal sums.
%C A318434 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e A318434 The a(3072) = 5 constant-sum split partitions:
%e A318434   (21111111111)
%e A318434   (21111)(111111)
%e A318434   (211)(1111)(1111)
%e A318434   (21)(111)(111)(111)
%e A318434   (2)(11)(11)(11)(11)(11)
%t A318434 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]]}];
%t A318434 Table[Length[Select[comps[If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]],SameQ@@Total/@#&]],{n,100}]
%Y A318434 Cf. A001970, A056239, A063834, A296150, A316223, A317545, A317546, A319002.
%Y A318434 Cf. A316245, A317508, A317715, A318683, A318684, A319794.
%K A318434 nonn
%O A318434 1,4
%A A318434 _Gus Wiseman_, Sep 29 2018