A279984 Positions of the prime numbers in the sequence of numbers that are not perfect powers (A007916).

1, 2, 3, 5, 7, 9, 12, 14, 18, 22, 24, 28, 32, 34, 38, 43, 49, 51, 56, 60, 62, 68, 71, 77, 85, 88, 90, 94, 96, 100, 112, 115, 121, 123, 132, 134, 140, 146, 150, 155, 161, 163, 173, 175, 178, 180, 192, 203, 206, 208, 212, 218, 220, 229, 234, 240, 246, 248, 254

Offset: 1

Author

Gus Wiseman, Dec 24 2016

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A007916, A279944.

Programs

Mathematica

nn=100;rads=Select[Range[2,nn],GCD@@FactorInteger[#][[All,2]]===1&];
Table[Position[rads,Prime[n]][[1,1]],{n,PrimePi[nn]}]

PARI

lista(nn) = Vec(select(x->isprime(x), Vec(select(x->(!ispower(x)&&x>1), [1..nn])), 1)); \\ Michel Marcus, May 04 2018

Python

from sympy import prime, mobius, integer_nthroot
def A279984(n): return int((p:=prime(n))-1+sum(mobius(k)*(integer_nthroot(p,k)[0]-1) for k in range(2,p.bit_length()))) # Chai Wah Wu, Oct 12 2024

Formula

A007916(a(n)) = A000040(n).