A378038 First differences of A112925 = greatest squarefree number < prime(n).

1, 1, 3, 4, 1, 4, 2, 5, 4, 4, 5, 4, 3, 4, 5, 7, 1, 7, 4, 1, 7, 4, 5, 8, 2, 5, 4, 1, 4, 12, 7, 4, 4, 8, 3, 6, 6, 5, 4, 8, 1, 11, 1, 4, 2, 13, 12, 4, 1, 4, 7, 1, 10, 6, 7, 5, 2, 5, 4, 4, 9, 14, 5, 1, 3, 16, 5, 11, 1, 2, 9, 8, 5, 6, 5, 4, 9, 4, 8, 11, 1, 11, 1, 7

Offset

1,3

Links

Table of n, a(n) for n=1..84.

Mathematica

Differences[Table[NestWhile[#-1&, Prime[n]-1, !SquareFreeQ[#]&], {n, 100}]]

Crossrefs

First differences of A112925, restriction of A070321, differences A378085.

For prime powers we have A377781, opposite A377703.

The nonsquarefree opposite is A377784 (differences of A377783), restriction of A378039.

The nonsquarefree version is A378034, first differences of A378032.

The opposite is A378037, differences of A112926.

The unrestricted opposite is A378087, differences of A067535.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.

A061398 counts squarefree numbers between primes, zeros A068360.

A061399 counts nonsquarefree numbers between primes, zeros A068361.

Cf. A007674, A013928, A045882, A053797, A053806, A072284, A073247, A120327, A280892, A378036, A378040, A378084.

Sequence in context: A131129 A087694 A010262 * A201516 A105579 A124446

Adjacent sequences: A378035 A378036 A378037 * A378039 A378040 A378041

Keyword

nonn

Author

Gus Wiseman, Dec 04 2024

Status

approved