A378618 Sum of nonsquarefree numbers between prime(n) and prime(n+1).

0, 4, 0, 17, 12, 16, 18, 20, 104, 0, 68, 40, 0, 89, 199, 110, 60, 127, 68, 72, 151, 161, 172, 278, 297, 0, 104, 108, 112, 849, 128, 403, 0, 579, 150, 461, 322, 164, 680, 351, 180, 561, 192, 196, 198, 819, 648, 449, 228, 232, 470, 240, 1472, 508, 521, 532, 270

Offset: 1

Author

Gus Wiseman, Dec 09 2024

Keywords

• nonn

Examples

			The nonsquarefree numbers between prime(24) = 89 and prime(25) = 97 are {90, 92, 96}, so a(24) = 278.
		

Crossrefs

For prime instead of nonsquarefree we have A001043.

For composite instead of nonsquarefree we have A054265.

Zeros are A068361.

A000040 lists the primes, differences A001223, seconds A036263.

A070321 gives the greatest squarefree number up to n.

A071403 counts squarefree numbers up to prime(n), restriction of A013928.

A120327 gives the least nonsquarefree number >= n.

A378086 counts nonsquarefree numbers up to prime(n), restriction of A057627.

For squarefree numbers (A005117, differences A076259) between primes:

- length is A061398, zeros A068360

- min is A112926, differences A378037

- max is A112925, differences A378038

- sum is A373197

For nonsquarefree numbers (A013929, differences A078147) between primes:

- length is A061399

- min is A377783 (differences A377784), union A378040

- max is A378032 (differences A378034), restriction of A378033 (differences A378036)

- sum is A378618 (this)

Cf. A007674, A045882, A053806, A067535, A072284, A073247, A179211, A224363, A373198, A377049, A377431.

Programs

Mathematica

Table[Total[Select[Range[Prime[n],Prime[n+1]],!SquareFreeQ[#]&]],{n,100}]