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

1,2

Links

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

Formula

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

Mathematica

Table[PrimePi[NextPrime[n]], {n, Select[Range[2500], #==1||GCD@@FactorInteger[#][[;; , 2]]>1&]}]

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.

Sequence in context: A168056 A122800 A227950 * A063202 A058020 A069201

Adjacent sequences: A378353 A378354 A378355 * A378357 A378358 A378359

Keyword

nonn

Author

Gus Wiseman, Dec 05 2024

Extensions

Mathematica program corrected by Sean A. Irvine and Harvey P. Dale, Jan 30 2026

Status

approved