A179705 - OEIS

%I #15 Jul 06 2020 02:40:14

%S 3456,16000,17496,43904,170368,273375,281216,625000,628864,750141,

%T 877952,1557376,2109375,2910897,3121792,3813248,4804839,6483584,

%U 6588344,8821888,10176896,10744731,13289344,15000633,19056256

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

%H T. D. Noe, <a href="/A179705/b179705.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(7) - P(10) = A085541 * A085967 - P(10) = 0.000454..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={3,7}; Select[Range[100000],f]

%t 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 (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 Cf. A085541, A085967.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 24 2010