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

1,6

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, ...

Links

Table of n, a(n) for n=1..67.

Formula

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

Example

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

Mathematica

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

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.

Sequence in context: A318237 A201572 A261468 * A001734 A342373 A173067

Adjacent sequences: A378363 A378365 A378366 * A378369 A378370 A378371

Keyword

nonn,new

Author

Gus Wiseman, Nov 29 2024

Status

approved