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

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, Prime Signatures

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

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 *)

Prog

(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

Crossrefs

Cf. A085541, A085967.

Sequence in context: A341553 A340437 A278270 * A234893 A251485 A082242

Adjacent sequences: A179702 A179703 A179704 * A179706 A179707 A179708

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Status

approved