A378373 Number of composite numbers (A002808) between consecutive nonsquarefree numbers (A013929), exclusive.

1, 0, 1, 2, 0, 0, 2, 0, 1, 0, 1, 3, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 2, 2, 1, 0, 2, 0, 1, 3, 0, 1, 3, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 1, 3, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 1, 0, 1, 0, 2, 2, 3, 0, 1, 2, 0, 0, 3, 2, 0, 2, 3, 3, 2, 0, 1, 2

Offset

1,4

Comments

All terms are 0, 1, 2, or 3 (cf. A078147).

The inclusive version is a(n) + 2.

The nonsquarefree numbers begin: 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, ...

Links

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

Example

The composite numbers counted by a(n) form the following set partition of A120944:
{6}, {}, {10}, {14,15}, {}, {}, {21,22}, {}, {26}, {}, {30}, {33,34,35}, {38,39}, ...

Mathematica

v=Select[Range[100], !SquareFreeQ[#]&];
Table[Length[Select[Range[v[[i]]+1, v[[i+1]]-1], CompositeQ]], {i, Length[v]-1}]

Crossrefs

For prime (instead of nonsquarefree) we have A046933.

For squarefree (instead of nonsquarefree) we have A076259(n)-1.

For prime power (instead of nonsquarefree) we have A093555.

For prime instead of composite we have A236575.

For nonprime prime power (instead of nonsquarefree) we have A378456.

For perfect power (instead of nonsquarefree) we have A378614, primes A080769.

A002808 lists the composite numbers.

A005117 lists the squarefree numbers, differences A076259.

A013929 lists the nonsquarefree numbers, differences A078147.

A073247 lists squarefree numbers with nonsquarefree neighbors.

A120944 lists squarefree composite numbers.

A377432 counts perfect-powers between primes, zeros A377436.

A378369 gives distance to the next nonsquarefree number (A120327).

Cf. A065890, A067535, A067871, A080101, A081221, A151800, A243348, A366833, A377046, A378033, A378039, A378086.

Sequence in context: A271223 A260944 A101670 * A351978 A219491 A305714

Adjacent sequences: A378370 A378371 A378372 * A378374 A378375 A378376

Keyword

nonn

Author

Gus Wiseman, Dec 02 2024

Status

approved