A378371 Distance between n and the least non prime power >= n, allowing 1.

0, 4, 3, 2, 1, 0, 3, 2, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0

Offset: 1

Author

Gus Wiseman, Nov 28 2024

Keywords

• nonn

Comments

Non prime powers allowing 1 (A361102) are numbers that are not a prime power (A246655), namely 1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, ...

Examples

			The least non prime power >= 4 is 6, so a(4) = 2.
		

Crossrefs

Sequences obtained by adding n to each term are placed in parentheses below.

For prime we have A007920 (A151800), strict A013632.

For composite we have A010051 (A113646 except initial terms).

For perfect power we have A074984 (A377468)

For squarefree we have A081221 (A067535).

For nonsquarefree we have (A120327).

For non perfect power we have A378357 (A378358).

The opposite version is A378366 (A378367).

For prime power we have A378370, strict A377282 (A000015).

This sequence is A378371 (A378372).

A000040 lists the primes, differences A001223.

A000961 and A246655 list the prime powers, differences A057820.

A024619 and A361102 list the non prime powers, differences A375708 and A375735.

Prime powers between primes: A053607, A080101, A304521, A366833, A377057.

Cf. A007916, A053707, A065514, A276781 (A031218), A343249, A345531, A376596, A376597, A377051, A377054, A377289, A378457.

Programs

Mathematica

Table[NestWhile[#+1&,n,PrimePowerQ[#]&]-n,{n,100}]

Formula

a(n) = A378372(n) - n.