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

1,2

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A007916, A279944.

Sequence in context: A293262 A348623 A200049 * A184017 A024195 A071423

Adjacent sequences: A279981 A279982 A279983 * A279985 A279986 A279987

Keyword

nonn

Author

Gus Wiseman, Dec 24 2016

Status

approved