A362965 Number of primes <= the n-th prime power.

1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 30, 31, 31, 32, 33, 34, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 53, 54, 54, 55, 56, 57, 58, 59, 60

Offset

1,2

Comments

Also, number of distinct primes among the first n prime powers (cf. A246655).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000720(A246655(n)).

Mathematica

A362965list[upto_]:=PrimePi[Select[Range[upto], PrimePowerQ]]; A362965list[500] (* Paolo Xausa, Jun 29 2023 *)

Prog

(PARI) apply(primepi, [p| p <- [1..300], isprimepower(p)]) \\ Michel Marcus, Jun 04 2023

Crossrefs

Cf. A000961, A000720, A246655, A366833 (run lengths).

Sequence in context: A239105 A302255 A218446 * A102548 A343174 A340205

Adjacent sequences: A362962 A362963 A362964 * A362966 A362967 A362968

Keyword

nonn

Author

Max Alekseyev, Jun 03 2023

Status

approved