A325770 Number of distinct nonempty contiguous subsequences of the integer partition with Heinz number n.

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 5, 1, 3, 3, 4, 1, 5, 1, 5, 3, 3, 1, 7, 2, 3, 3, 5, 1, 6, 1, 5, 3, 3, 3, 8, 1, 3, 3, 7, 1, 6, 1, 5, 5, 3, 1, 9, 2, 5, 3, 5, 1, 7, 3, 7, 3, 3, 1, 9, 1, 3, 5, 6, 3, 6, 1, 5, 3, 6, 1, 11, 1, 3, 5, 5, 3, 6, 1, 9, 4, 3, 1, 9, 3, 3, 3

Offset: 1

Author

Gus Wiseman, May 20 2019

Keywords

• nonn

Comments

After a(1) = 0, first differs from A305611 at a(42) = 6, A305611(42) = 7.

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

Examples

			The a(84) = 9 distinct nonempty contiguous subsequences of (4,2,1,1) are (1), (2), (4), (1,1), (2,1), (4,2), (2,1,1), (4,2,1), (4,2,1,1).
		

Crossrefs

Cf. A002865, A103295, A112798, A124771, A276024, A325765, A325768, A325769, A335519, A335838.

Programs

Mathematica

Table[Length[Union[ReplaceList[If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]],{_,s__,_}:>{s}]]],{n,30}]

Formula

a(n) = A335519(n) - 1.

Extensions

Name corrected by Gus Wiseman, Jun 27 2020