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

3456, 16000, 17496, 43904, 170368, 273375, 281216, 625000, 628864, 750141, 877952, 1557376, 2109375, 2910897, 3121792, 3813248, 4804839, 6483584, 6588344, 8821888, 10176896, 10744731, 13289344, 15000633, 19056256

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Will Nicholes, Prime Signatures

Crossrefs

Cf. A085541, A085967.

Programs

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={3,7}; Select[Range[100000],f]
With[{nn=25},Take[Union[#[[1]]^7 #[[2]]^3&/@(Flatten[{#,Reverse[ #]}&/@ Subsets[ Prime[Range[nn]],{2}],1])],nn]] (* Harvey P. Dale, Jan 01 2016 *)

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

Formula

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