cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A179705 Numbers of the form p^7*q^3 where p and q are distinct primes.

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%I A179705 #15 Jul 06 2020 02:40:14
%S A179705 3456,16000,17496,43904,170368,273375,281216,625000,628864,750141,
%T A179705 877952,1557376,2109375,2910897,3121792,3813248,4804839,6483584,
%U A179705 6588344,8821888,10176896,10744731,13289344,15000633,19056256
%N A179705 Numbers of the form p^7*q^3 where p and q are distinct primes.
%H A179705 T. D. Noe, <a href="/A179705/b179705.txt">Table of n, a(n) for n = 1..1000</a>
%H A179705 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%F A179705 Sum_{n>=1} 1/a(n) = P(3)*P(7) - P(10) = A085541 * A085967 - P(10) = 0.000454..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%t A179705 f[n_]:=Sort[Last/@FactorInteger[n]]=={3,7}; Select[Range[100000],f]
%t A179705 With[{nn=25},Take[Union[#[[1]]^7 #[[2]]^3&/@(Flatten[{#,Reverse[ #]}&/@ Subsets[ Prime[Range[nn]],{2}],1])],nn]] (* _Harvey P. Dale_, Jan 01 2016 *)
%o A179705 (PARI) list(lim)=my(v=List(),t);forprime(p=2, (lim\8)^(1/7), t=p^7;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 A179705 Cf. A085541, A085967.
%K A179705 nonn
%O A179705 1,1
%A A179705 _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010