A378370 Distance between n and the least prime power >= n, allowing 1.

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

Offset

1,14

Comments

Prime powers allowing 1 are listed by A000961.

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A000015(n) - n.

a(n) = A377282(n - 1) - 1 for n > 1.

Mathematica

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

Crossrefs

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

For prime instead of prime power we have A007920 (A007918), strict A013632.

For perfect power we have A074984 (A377468), opposite A069584 (A081676).

For squarefree we have A081221 (A067535).

The restriction to the prime numbers is A377281 (A345531).

The strict version is A377282 = a(n) + 1.

For non prime power instead of prime power we have A378371 (A378372).

The opposite version is A378457, strict A276781.

A000015 gives the least prime power >= n, opposite A031218.

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.

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

Cf. A001597, A053707, A065514, A065890, A343249, A376596, A376597, A377051, A377054, A377289, A377781.

Sequence in context: A096608 A155102 A237621 * A214625 A363339 A334195

Adjacent sequences: A378366 A378367 A378369 * A378371 A378372 A378373

Keyword

nonn,new

Author

Gus Wiseman, Nov 27 2024

Status

approved