A378367 Greatest non prime power <= n, allowing 1.

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

Offset: 1

Author

Gus Wiseman, Nov 29 2024

Keywords

• nonn
• changed

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 greatest non prime power <= 7 is 6, so a(7) = 6.
		

Crossrefs

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

For prime we have A007917 (A064722).

For nonprime we have A179278 (A010051 almost).

For perfect power we have A081676 (A069584).

For squarefree we have A070321.

For nonsquarefree we have A378033.

For non perfect power we have A378363.

The opposite is A378372, subtracting n A378371.

For prime power we have A031218 (A276781 - 1).

Subtracting from n gives (A378366).

A000015 gives the least prime power >= n (A378370).

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.

A151800 gives the least prime > n (A013632), weak version A007918 (A007920).

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

Cf. A007916, A065514, A113646, A345531 (A377281), A377051, A377054, A377282, A377468 (A074984), A378358, A378457.

Cf. A356068.

Programs

Mathematica

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

Formula

a(n) = n - A378366(n).

a(n) = A361102(A356068(n)). - Ridouane Oudra, Aug 22 2025