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%I #23 Jul 07 2020 06:00:47
%S 2592,3888,20000,50000,76832,151875,253125,268912,468512,583443,
%T 913952,1361367,2576816,2672672,3557763,4170272,5940688,6940323,
%U 7503125,8954912,10504375,13045131,20295603,22632992,22717712,29552672,30074733
%N Numbers of the form p^4*q^5 where p and q are two distinct primes.
%C Subsequence of A046312 and of A137493. - _R. J. Mathar_, Jul 27 2010
%H T. D. Noe, <a href="/A179702/b179702.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(4)*P(5) - P(9) = A085964 * A085965 - A085969 = 0.000748..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%t fQ[n_] := Sort[Last /@ FactorInteger @n] == {4, 5}; Select[ Range@ 31668000, fQ] (* fixed by _Robert G. Wilson v_, Aug 26 2010 *)
%t lst = {}; Do[ If[p != q, AppendTo[lst, Prime@p^4*Prime@q^5]], {p, 12}, {q, 10}]; Take[ Sort@ Flatten@ lst, 27] (* _Robert G. Wilson v_, Aug 26 2010 *)
%t Take[Union[First[#]^4 Last[#]^5&/@Flatten[Permutations/@Subsets[ Prime[ Range[30]],{2}],1]],30] (* _Harvey P. Dale_, Jan 01 2012 *)
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2, (lim\16)^(1/5), t=p^5;forprime(q=2, (lim\t)^(1/4), if(p==q, next);listput(v,t*q^4))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 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, A179694, A179695, A179696, A179698, A179699, A179700.
%Y Cf. A085964, A085965, A085969.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010
%E Edited and extended by _Ray Chandler_ and _R. J. Mathar_, Jul 26 2010
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