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A246549
Prime powers p^e where p is a prime and e >= 3 (prime powers without 1, the primes, or the squares of primes).
7
8, 16, 27, 32, 64, 81, 125, 128, 243, 256, 343, 512, 625, 729, 1024, 1331, 2048, 2187, 2197, 2401, 3125, 4096, 4913, 6561, 6859, 8192, 12167, 14641, 15625, 16384, 16807, 19683, 24389, 28561, 29791, 32768, 50653, 59049, 65536, 68921, 78125, 79507, 83521, 103823, 117649, 130321, 131072, 148877, 161051, 177147, 205379
OFFSET
1,1
COMMENTS
Consists of 8 and the terms of A088247. - R. J. Mathar, Sep 01 2014
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = Sum_{p prime} 1/(p^2*(p-1)) = A152441. - Amiram Eldar, Oct 24 2020
MATHEMATICA
With[{nn=60}, Take[Union[Flatten[Table[p^Range[3, nn/3], {p, Prime[ Range[ nn]]}]]], nn]] (* Harvey P. Dale, Dec 10 2015 *)
PROG
(PARI) for(n=1, 10^6, if(isprimepower(n)>=3, print1(n, ", ")));
(PARI) m=10^6; v=[]; forprime(p=2, m^(1/3), e=3; while(p^e<=m, v=concat(v, p^e); e++)); v=vecsort(v) \\ Faster program. Jens Kruse Andersen, Aug 29 2014
(Python)
from math import isqrt
from sympy import primerange, integer_nthroot, primepi
def A246549(n):
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b+1, isqrt(x//c)+1), a+1)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b+1, integer_nthroot(x//c, m)[0]+1), a+1) for d in g(x, a2, b2, c*b2, m-1)))
def f(x): return int(n+x-sum(primepi(integer_nthroot(x, k)[0]) for k in range(3, x.bit_length())))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return bisection(f, n, n) # Chai Wah Wu, Sep 11 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Aug 29 2014
STATUS
approved