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

1,2

Links

Table of n, a(n) for n=1..57.

Example

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

Mathematica

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

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.

Sequence in context: A375992 A233807 A302771 * A167350 A215669 A244310

Adjacent sequences: A378615 A378616 A378617 * A378620 A378626 A378629

Keyword

nonn,new

Author

Gus Wiseman, Dec 09 2024

Status

approved