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%I #14 May 05 2023 10:08:21
%S 1728,5832,8000,21952,85184,91125,125000,140608,250047,314432,421875,
%T 438976,778688,941192,970299,1560896,1601613,1906624,3176523,3241792,
%U 3581577,4410944,5000211,5088448,5359375,6644672
%N Numbers of the form p^6*q^3 where p and q are distinct primes.
%H T. D. Noe, <a href="/A179694/b179694.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>
%F Sum_{n>=1} 1/a(n) = P(3)*P(6) - P(9) = A085541 * A085966 - A085969 = 0.000978..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%F a(n) = A054753(n)^3. - _R. J. Mathar_, May 05 2023
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={3,6}; Select[Range[10^6], f]
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2, (lim\8)^(1/6), t=p^6;forprime(q=2, (lim\t)^(1/3), if(p==q, next);listput(v,t*q^3))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 24 2011
%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, A179692, A179693.
%Y Cf. A085541, A085966, A085969.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010
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