A302491 Prime numbers of squarefree index.

2, 3, 5, 11, 13, 17, 29, 31, 41, 43, 47, 59, 67, 73, 79, 83, 101, 109, 113, 127, 137, 139, 149, 157, 163, 167, 179, 181, 191, 199, 211, 233, 241, 257, 269, 271, 277, 283, 293, 313, 317, 331, 347, 349, 353, 367, 373, 389, 397, 401, 421, 431, 439, 443, 449, 461

Offset: 1

Author

Gus Wiseman, Apr 08 2018

Keywords

• nonn
• easy

Comments

A prime index of n is a number m such that prime(m) divides n.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000961, A001222, A005117, A007097, A056239, A063834, A275024, A281113, A302242, A302478.

Programs

Maple

map(ithprime, select(numtheory:-issqrfree, [$1..500])); # Robert Israel, Nov 06 2023

Mathematica

Prime/@Select[Range[100],SquareFreeQ]

PARI

forprime(p=1, 500, if(issquarefree(primepi(p)), print1(p, ", "))) \\ Felix Fröhlich, Apr 10 2018

PARI

list(lim)=my(v=List(),k); forprime(p=2,lim\1, if(issquarefree(k++), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Aug 03 2023

Formula

a(n) = A000040(A005117(n)).

a(n) ~ kn log n, where k = Pi^2/6. - Charles R Greathouse IV, Aug 03 2023