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A087797
Primes, squares of primes and cubes of primes.
4
2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241
OFFSET
1,1
COMMENTS
Union of A000040 and A168363. - Chai Wah Wu, Aug 09 2024
LINKS
FORMULA
a(n) ~ n log n. - Charles R Greathouse IV, Oct 19 2015
MATHEMATICA
m=400; Union[Prime[Range[PrimePi[m]]], Prime[Range[PrimePi[m^(1/2)]]]^2, Prime[Range[PrimePi[m^(1/3)]]]^3] (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)
With[{nn=70}, Take[Union[Flatten[{#, #^2, #^3}&/@Prime[Range[nn]]]], nn]] (* Harvey P. Dale, Oct 16 2012 *)
PROG
(PARI) is(n)=my(t=isprimepower(n)); t && t<4 \\ Charles R Greathouse IV, Oct 19 2015
(Python)
from math import isqrt
from sympy import primepi, integer_nthroot
def A087797(n):
def f(x): return n+x-primepi(x)-primepi(isqrt(x))-primepi(integer_nthroot(x, 3)[0])
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return int(m) # Chai Wah Wu, Aug 09 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Oct 10 2003
STATUS
approved