A377781 First differences of A065514(n) = greatest number < prime(n) that is 1 or a prime-power.

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

Offset: 1

Author

Gus Wiseman, Nov 14 2024

Keywords

• nonn

Comments

Note 1 is a power of a prime but not a prime-power.

Crossrefs

Differences of A065514, which is the restriction of A031218 (differences A377782).

The opposite is A377703 (restriction of A000015), differences of A345531.

The opposite for nonsquarefree is A377784, differences of A377783.

For nonsquarefree we have A378034, differences of A378032 (restriction of A378033).

The opposite for squarefree is A378037, differences of A112926 (restriction of A067535).

For squarefree we have A378038, differences of A112925 (restriction of A070321).

A000040 lists the primes, differences A001223.

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

A024619 lists the non-prime-powers, differences A375735, seconds A376599.

A361102 lists the non-powers of primes, differences A375708.

Prime-powers between primes:

- A053607 primes

- A080101 count (exclusive)

- A304521 by bits

- A366833 count

- A377057 positive

- A377286 zero

- A377287 one

- A377288 two

Cf. A001597, A007916, A008864, A053289, A120327, A343249, A375706, A377281, A377282, A377289.

Programs

Mathematica

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