A179668 Products of the 8th power of a prime and a distinct prime (p^8*q).

768, 1280, 1792, 2816, 3328, 4352, 4864, 5888, 7424, 7936, 9472, 10496, 11008, 12032, 13122, 13568, 15104, 15616, 17152, 18176, 18688, 20224, 21248, 22784, 24832, 25856, 26368, 27392, 27904, 28928, 32512, 32805, 33536, 35072, 35584, 38144, 38656, 40192

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, Prime Signatures

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 8}; Select[Range[40000], f]
With[{nn=40}, Take[Union[#[[1]]^8 #[[2]]&/@Flatten[Permutations/@Subsets[ Prime[Range[nn]], {2}], 1]], nn]] (* Harvey P. Dale, Jan 20 2016 *)

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\2)^(1/8), t=p^8; forprime(q=2, lim\t, if(p==q, next); listput(v, t*q))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
(Python)
from sympy import primepi, primerange, integer_nthroot
def A179668(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum(primepi(x//p**8) for p in primerange(integer_nthroot(x, 8)[0]+1))+primepi(integer_nthroot(x, 9)[0])
    return bisection(f, n, n) # Chai Wah Wu, Feb 21 2025

Crossrefs

Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667.

Sequence in context: A219225 A045082 A257414 * A219317 A281238 A268808

Adjacent sequences: A179665 A179666 A179667 * A179669 A179670 A179671

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 23 2010

Status

approved