cp's OEIS Frontend

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

%I A179668 #25 Feb 21 2025 19:40:12
%S A179668 768,1280,1792,2816,3328,4352,4864,5888,7424,7936,9472,10496,11008,
%T A179668 12032,13122,13568,15104,15616,17152,18176,18688,20224,21248,22784,
%U A179668 24832,25856,26368,27392,27904,28928,32512,32805,33536,35072,35584,38144,38656,40192
%N A179668 Products of the 8th power of a prime and a distinct prime (p^8*q).
%H A179668 T. D. Noe, <a href="/A179668/b179668.txt">Table of n, a(n) for n = 1..1000</a>
%H A179668 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%t A179668 f[n_]:=Sort[Last/@FactorInteger[n]]=={1,8}; Select[Range[40000], f]
%t A179668 With[{nn=40},Take[Union[#[[1]]^8 #[[2]]&/@Flatten[Permutations/@Subsets[ Prime[Range[nn]],{2}],1]],nn]] (* _Harvey P. Dale_, Jan 20 2016 *)
%o A179668 (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
%o A179668 (Python)
%o A179668 from sympy import primepi, primerange, integer_nthroot
%o A179668 def A179668(n):
%o A179668     def bisection(f,kmin=0,kmax=1):
%o A179668         while f(kmax) > kmax: kmax <<= 1
%o A179668         kmin = kmax >> 1
%o A179668         while kmax-kmin > 1:
%o A179668             kmid = kmax+kmin>>1
%o A179668             if f(kmid) <= kmid:
%o A179668                 kmax = kmid
%o A179668             else:
%o A179668                 kmin = kmid
%o A179668         return kmax
%o A179668     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])
%o A179668     return bisection(f,n,n) # _Chai Wah Wu_, Feb 21 2025
%Y A179668 Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667.
%K A179668 nonn
%O A179668 1,1
%A A179668 _Vladimir Joseph Stephan Orlovsky_, Jul 23 2010