login
A179702
Numbers of the form p^4*q^5 where p and q are two distinct primes.
5
2592, 3888, 20000, 50000, 76832, 151875, 253125, 268912, 468512, 583443, 913952, 1361367, 2576816, 2672672, 3557763, 4170272, 5940688, 6940323, 7503125, 8954912, 10504375, 13045131, 20295603, 22632992, 22717712, 29552672, 30074733
OFFSET
1,1
COMMENTS
Subsequence of A046312 and of A137493. - R. J. Mathar, Jul 27 2010
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = P(4)*P(5) - P(9) = A085964 * A085965 - A085969 = 0.000748..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020
MATHEMATICA
fQ[n_] := Sort[Last /@ FactorInteger @n] == {4, 5}; Select[ Range@ 31668000, fQ] (* fixed by Robert G. Wilson v, Aug 26 2010 *)
lst = {}; Do[ If[p != q, AppendTo[lst, Prime@p^4*Prime@q^5]], {p, 12}, {q, 10}]; Take[ Sort@ Flatten@ lst, 27] (* Robert G. Wilson v, Aug 26 2010 *)
Take[Union[First[#]^4 Last[#]^5&/@Flatten[Permutations/@Subsets[ Prime[ Range[30]], {2}], 1]], 30] (* Harvey P. Dale, Jan 01 2012 *)
PROG
(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\16)^(1/5), t=p^5; forprime(q=2, (lim\t)^(1/4), if(p==q, next); listput(v, t*q^4))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and extended by Ray Chandler and R. J. Mathar, Jul 26 2010
STATUS
approved