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A279984
Positions of the prime numbers in the sequence of numbers that are not perfect powers (A007916).
2
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 24 2016
STATUS
approved