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%I #19 Nov 15 2020 16:49:10
%S 432,648,2000,5000,5488,10125,16875,19208,21296,27783,35152,64827,
%T 78608,107811,109744,117128,177957,194672,214375,228488,300125,390224,
%U 395307,397953,476656,555579,668168,771147,810448,831875
%N Products of the 4th power of a prime and a distinct prime of power 3 (p^4*q^3).
%H T. D. Noe, <a href="/A179666/b179666.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>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%F Sum_{n>=1} 1/a(n) = P(3)*P(4) - P(7) = A085541 * A085964 - A085967 = 0.005171..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={3,4}; Select[Range[10^6], f]
%t With[{nn=40},Select[Flatten[{#[[1]]^4 #[[2]]^3,#[[1]]^3 #[[2]]^4}&/@ Subsets[ Prime[Range[nn]],{2}]]//Union,#<=16nn^3&]] (* _Harvey P. Dale_, Nov 15 2020 *)
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2,(lim\8)^(1/4),t=p^4;forprime(q=2,(lim\t)^(1/3),if(p==q,next);listput(v,t*q^3)));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%Y Cf. A046308, A030638, A007774.
%Y Cf. A085541, A085964, A085967.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 23 2010
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