A246549 Prime powers p^e where p is a prime and e >= 3 (prime powers without 1, the primes, or the squares of primes).

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

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

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

Cf. A000961, A152441, A246547, A246550.

Sequence in context: A390540 A111307 A386632 * A076405 A099997 A053093

Adjacent sequences: A246546 A246547 A246548 * A246550 A246551 A246552

Keyword

nonn

Author

Joerg Arndt, Aug 29 2014

Status

approved