A378616 Greatest non prime power <= prime(n).

1, 1, 1, 6, 10, 12, 15, 18, 22, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 96, 100, 102, 106, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238, 240, 250, 255, 262, 268, 270

Offset: 1

Author

Gus Wiseman, Dec 06 2024

Keywords

• nonn

Comments

Conjecture: Equal to A006093(n) = prime(n) - 1 except at terms of A159611.

Examples

			The first number line below shows the non prime powers. The second shows the primes:
--1-------------6----------10----12----14-15-------18----20-21-22----24--
=====2==3====5=====7==========11====13==========17====19==========23=====
		

Crossrefs

For nonprime instead of non prime power we have A156037.

Restriction of A378367.

Lengths are A378615.

For nonsquarefree: A378032 (diffs A378034), restriction of A378033 (diffs A378036).

A000040 lists the primes, differences A001223

A000961 and A246655 list the prime powers, differences A057820.

A024619 lists the non prime powers, differences A375735, seconds A376599.

A080101 counts prime powers between primes (exclusive), inclusive A366833.

A361102 lists the non powers of primes, differences A375708.

Prime powers between primes:

- A377057 positive

- A377286 zero

- A377287 one

- A377288 two

Cf. A006093, A053607, A143731, A159611, A304521, A343249, A345531, A356068, A368748, A377281, A377289, A377703, A377781.

Programs

Mathematica

Table[Max[Select[Range[Prime[n]],Not@*PrimePowerQ]],{n,100}]