A378356 Prime index of the next prime after the n-th perfect power.

1, 3, 5, 5, 7, 10, 10, 12, 12, 16, 19, 23, 26, 31, 31, 32, 35, 40, 45, 48, 49, 54, 55, 62, 67, 69, 73, 79, 86, 93, 98, 100, 106, 115, 123, 130, 138, 147, 155, 163, 169, 173, 182, 192, 201, 211, 218, 220, 229, 241, 252, 264, 270, 275, 284, 296, 307, 310, 320

Offset: 1

Author

Gus Wiseman, Dec 05 2024

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

First differences are A080769.

Union is A378365.

A000040 lists the primes, differences A001223.

A000961 lists the powers of primes, differences A057820.

A001597 lists the perfect powers, differences A053289.

A007916 lists the non perfect powers, differences A375706.

A069623 counts perfect powers <= n.

A076411 counts perfect powers < n.

A377432 counts perfect powers between primes, see A377434, A377436, A377466.

A378249 gives the least perfect power > prime(n), restriction of A377468.

Cf. A045542, A052410, A065514, A068361, A076412, A081676, A216765, A345531, A377283, A378035, A378250, A378251, A378253.

Programs

Mathematica

Table[PrimePi[NextPrime[n]],{n,Select[Range[1000],perpowQ]}]

Formula

a(n) = A000720(A001597(n)) + 1.