A179692 - OEIS

%I #17 Feb 21 2025 19:39:16

%S 1536,2560,3584,5632,6656,8704,9728,11776,14848,15872,18944,20992,

%T 22016,24064,27136,30208,31232,34304,36352,37376,39366,40448,42496,

%U 45568,49664,51712,52736,54784,55808,57856,65024,67072,70144,71168,76288,77312,80384,83456

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

%H T. D. Noe, <a href="/A179692/b179692.txt">Table of n, a(n) for n = 1..1000</a>

%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,9}; Select[Range[90000], f]

%o (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 (Python)

%o from sympy import primepi, integer_nthroot, primerange

%o def A179692(n):

%o     def bisection(f,kmin=0,kmax=1):

%o         while f(kmax) > kmax: kmax <<= 1

%o         kmin = kmax >> 1

%o         while kmax-kmin > 1:

%o             kmid = kmax+kmin>>1

%o             if f(kmid) <= kmid:

%o                 kmax = kmid

%o             else:

%o                 kmin = kmid

%o         return kmax

%o     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     return bisection(f,n,n) # _Chai Wah Wu_, Feb 21 2025

%Y 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 nonn,changed

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010