A179702 Numbers of the form p^4*q^5 where p and q are two distinct primes.

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

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

Will Nicholes, Prime Signatures

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

Crossrefs

Cf. A006881, A007304, A065036, A085986, A085987, A092759, A178739, A179642, A179643, A179644, A179645, A179646, A179664, A179665, A179666, A179667, A179668, A179669, A179670, A179671, A179672, A179688, A179689, A179690, A179691, A179692, A179693, A179694, A179695, A179696, A179698, A179699, A179700.

Cf. A085964, A085965, A085969.

Sequence in context: A250241 A252152 A035894 * A258728 A326747 A156322

Adjacent sequences: A179699 A179700 A179701 * A179703 A179704 A179705

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Extensions

Edited and extended by Ray Chandler and R. J. Mathar, Jul 26 2010

Status

approved