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

1,4

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).

Links

Table of n, a(n) for n=1..87.

Formula

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

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A350338 A239707 A294928 * A305611 A325765 A032741

Adjacent sequences: A325767 A325768 A325769 * A325771 A325772 A325773

Keyword

nonn

Author

Gus Wiseman, May 20 2019

Extensions

Name corrected by Gus Wiseman, Jun 27 2020

Status

approved