A378372 Least non prime power >= n, allowing 1.

1, 6, 6, 6, 6, 6, 10, 10, 10, 10, 12, 12, 14, 14, 15, 18, 18, 18, 20, 20, 21, 22, 24, 24, 26, 26, 28, 28, 30, 30, 33, 33, 33, 34, 35, 36, 38, 38, 39, 40, 42, 42, 44, 44, 45, 46, 48, 48, 50, 50, 51, 52, 54, 54, 55, 56, 57, 58, 60, 60, 62, 62, 63, 65, 65, 66, 68

Offset: 1

Author

Gus Wiseman, Nov 29 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) = 6.
		

Crossrefs

Sequences obtained by subtracting n from each term are placed in parentheses below.

For prime power we have A000015 (A378370).

For squarefree we have A067535 (A081221).

For composite we have A113646 (A010051).

For nonsquarefree we have A120327.

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

Run-lengths are 1 and A375708.

For perfect power we have A377468 (A074984).

For non-perfect power we have A378358 (A378357).

The opposite is A378367, distance A378366.

This sequence is A378372 (A378371).

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. A001597, A007916, A031218 (A276781), A053707, A065514, A345531 (A377281), A377051, A377282, A377289, A378457.

Programs

Mathematica

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

Formula

a(n) = A378371(n) + n.