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A179692 Numbers of the form p^9*q where p and q are distinct primes.

%I A179692 #17 Feb 21 2025 19:39:16
%S A179692 1536,2560,3584,5632,6656,8704,9728,11776,14848,15872,18944,20992,
%T A179692 22016,24064,27136,30208,31232,34304,36352,37376,39366,40448,42496,
%U A179692 45568,49664,51712,52736,54784,55808,57856,65024,67072,70144,71168,76288,77312,80384,83456
%N A179692 Numbers of the form p^9*q where p and q are distinct primes.
%H A179692 T. D. Noe, <a href="/A179692/b179692.txt">Table of n, a(n) for n = 1..1000</a>
%H A179692 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%t A179692 f[n_]:=Sort[Last/@FactorInteger[n]]=={1,9}; Select[Range[90000], f]
%o A179692 (PARI) list(lim)=my(v=List(),t);forprime(p=2, (lim\2)^(1/9), t=p^9;forprime(q=2, lim\t, if(p==q, next);listput(v,t*q))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 24 2011
%o A179692 (Python)
%o A179692 from sympy import primepi, integer_nthroot, primerange
%o A179692 def A179692(n):
%o A179692     def bisection(f,kmin=0,kmax=1):
%o A179692         while f(kmax) > kmax: kmax <<= 1
%o A179692         kmin = kmax >> 1
%o A179692         while kmax-kmin > 1:
%o A179692             kmid = kmax+kmin>>1
%o A179692             if f(kmid) <= kmid:
%o A179692                 kmax = kmid
%o A179692             else:
%o A179692                 kmin = kmid
%o A179692         return kmax
%o A179692     def f(x): return n+x-sum(primepi(x//p**9) for p in primerange(integer_nthroot(x,9)[0]+1))+primepi(integer_nthroot(x,10)[0])
%o A179692     return bisection(f,n,n) # _Chai Wah Wu_, Feb 21 2025
%Y A179692 Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667, A179668, A179669, A179670, A179671, A179672, A179688, A179689, A179690, A179691.
%K A179692 nonn
%O A179692 1,1
%A A179692 _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010