A378457 Difference between n and the greatest prime power <= n, allowing 1.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 3, 4, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 0, 1, 2, 3, 4

Offset: 1

Author

Gus Wiseman, Nov 29 2024

Keywords

• nonn

Comments

Prime powers allowing 1 are listed by A000961.

Examples

			The greatest prime power <= 6 is 5, so a(6) = 1.
		

Crossrefs

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

For nonprime we have A010051 (almost) (A179278).

Subtracting from n gives (A031218).

For prime we have A064722 (A007917).

For perfect power we have A069584 (A081676).

For squarefree we have (A070321).

Adding one gives A276781.

For nonsquarefree we have (A378033).

For non perfect power we have (A378363).

For non prime power we have A378366 (A378367).

The opposite is A378370 = A377282-1.

A000015 gives the least prime power >= n.

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, weak version A007918.

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

Cf. A001597, A007920, A013632, A065514, A074984, A377051, A377054, A377281, A377289, A377468, A378357, A378371.

Programs

Mathematica

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

Formula

a(n) = n - A031218(n).

a(n) = A276781(n) - 1.