A376307 Run-sums of the sequence of first differences of squarefree numbers.

2, 2, 2, 3, 1, 2, 2, 6, 2, 6, 2, 2, 2, 2, 2, 2, 2, 3, 1, 4, 6, 2, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 3, 1, 2, 2, 6, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 3, 1, 3, 1, 4, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 3, 1, 2, 2, 6, 2, 6, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 6, 2, 2, 1, 3

Offset: 1

Author

Gus Wiseman, Sep 21 2024

Keywords

• nonn

Examples

			The sequence of squarefree numbers (A005117) is:
  1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...
The sequence of first differences (A076259) of squarefree numbers is:
  1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ...
with runs:
  (1,1),(2),(1,1),(3),(1),(2),(1,1),(2,2,2),(1,1),(3,3),(1,1),(2),(1,1), ...
with sums A376307 (this sequence).
		

Crossrefs

Run-sums of first differences of A005117.

Before taking run-sums we had A076259, ones A375927.

For the squarefree numbers themselves we have A373413.

For prime instead of squarefree numbers we have A373822, halved A373823.

For compression instead of run-sums we have A376305, ones A376342.

For run-lengths instead of run-sums we have A376306.

For prime-powers instead of squarefree numbers we have A376310.

For positions of first appearances instead of run-sums we have A376311.

A000040 lists the prime numbers, differences A001223.

A000961 and A246655 list prime-powers, first differences A057820.

A003242 counts compressed or anti-run compositions, ranks A333489.

A005117 lists squarefree numbers, differences A076259.

A013929 lists nonsquarefree numbers, differences A078147.

A116861 counts partitions by compressed sum, by compressed length A116608.

A274174 counts contiguous compositions, ranks A374249.

Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A373197, A373198, A375707.

Programs

Mathematica

Total/@Split[Differences[Select[Range[100],SquareFreeQ]]]