A118092 Odd primes raised to odd prime powers.

27, 125, 243, 343, 1331, 2187, 2197, 3125, 4913, 6859, 12167, 16807, 24389, 29791, 50653, 68921, 78125, 79507, 103823, 148877, 161051, 177147, 205379, 226981, 300763, 357911, 371293, 389017, 493039, 571787, 704969, 823543, 912673, 1030301

Offset

1,1

Comments

Subset of A053810 Prime powers of prime numbers. Subset of A000961 Prime powers. Subsets include A030078 Cubes of primes, A050997 Fifth powers of primes.

Links

Table of n, a(n) for n=1..34.

Formula

{p^q where p is in A065091 and q is in A065091}.

Sum_{n>=1} 1/a(n) = Sum_{p odd prime} P(p) - A051006 + 1/4 = 0.054745292329555814476..., where P(s) is the prime zeta function. - Amiram Eldar, Sep 13 2024

Mathematica

With[{prs=Prime[Range[2, 30]]}, Take[Union[First[#]^Last[#]&/@ Tuples[prs, 2]], 40]] (* Harvey P. Dale, Dec 23 2011 *)

Prog

(Python)
from sympy import primepi, integer_nthroot, primerange
def A118092(n):
    def f(x): return int(n+x-sum(primepi(integer_nthroot(x, p)[0])-1 for p in primerange(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 12 2024

Crossrefs

Cf. A000040, A000961, A030078, A050997, A051006, A053810, A065091.

Sequence in context: A125497 A179145 A369118 * A371189 A126272 A016755

Adjacent sequences: A118089 A118090 A118091 * A118093 A118094 A118095

Keyword

easy,nonn

Author

Jonathan Vos Post, May 11 2006

Extensions

Extended by Ray Chandler, Oct 28 2008

Status

approved