A024620 Positions of primes among the powers of primes (A000961).

2, 3, 5, 6, 9, 10, 12, 13, 14, 17, 18, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 93, 94

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A025474(a(n)) = 1. - Reinhard Zumkeller, May 01 2015

a(n) = A001222(A056604(n)) + 1. - Eric Desbiaux, Dec 02 2018

From Ridouane Oudra, Oct 18 2020: (Start)

a(n) = A027883(n) + 1;

a(n) = A025528(A000040(n)) + 1;

a(n) = A065515(A000040(n)). (End)

Mathematica

a[n_] := PrimeOmega[LCM @@ Range@Prime@n] + 1; Array[a, 100] (* Amiram Eldar, Dec 02 2018 *)

Prog

(PARI) lista(nn) = my(powpr = select((i->((omega(i)==1) || (i==1))), [1..nn])); for (i = 1, #powpr, if (isprime(powpr[i]), print1(i, ", ")); ); \\ Michel Marcus, Jun 03 2021
(Haskell)
a024620 n = a024620_list !! (n-1)
a024620_list = filter ((== 1) . a025474) [1..]
-- Reinhard Zumkeller, May 01 2015
(Python)
from sympy import prime, primepi, integer_nthroot
def A024620(n):
    x = prime(n)
    return n+1+sum(primepi(integer_nthroot(x, k)[0]) for k in range(2, x.bit_length())) # Chai Wah Wu, Nov 05 2024

Crossrefs

Complement of A024621.

Cf. A001222 (bigomega), A025474, A056604, A027883.

Cf. A025528, A065515, A000040.

Sequence in context: A018762 A059746 A362030 * A232527 A188375 A047331

Adjacent sequences: A024617 A024618 A024619 * A024621 A024622 A024623

Keyword

nonn

Author

Clark Kimberling

Status

approved