A190114 Numbers with prime factorization p^2*q^2*r^5 where p, q, and r are distinct primes.

7200, 14112, 24300, 34848, 39200, 47628, 48672, 83232, 96800, 103968, 112500, 117612, 135200, 152352, 164268, 189728, 231200, 242208, 264992, 276768, 280908, 288800, 297675, 350892, 394272, 423200, 453152, 484128, 514188, 532512, 566048

Offset

1,1

Links

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

Will Nicholes, List of prime signatures, 2010.

Index to sequences related to prime signature.

Formula

Sum_{n>=1} 1/a(n) = P(2)^2*P(5)/2 - P(2)*P(8)/2 - P(4)*P(5)/2 - P(2)*P(7) + P(9) = 0.00053812627050585644544..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 5}; Select[Range[900000], f]
With[{upto=600000}, Select[#[[1]]^2 #[[2]]^2 #[[3]]^5&/@ Flatten[ Permutations/@ Subsets[Prime[Range[Ceiling[Surd[upto, 5]+1]]], {3}], 1]// Union, #<=upto&]] (* Harvey P. Dale, Jul 29 2018 *)

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\36)^(1/5), t1=p^5; forprime(q=2, sqrt(lim\t1), if(p==q, next); t2=t1*q^2; forprime(r=q+1, sqrt(lim\t2), if(p==r, next); listput(v, t2*r^2)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A179665, A190011, A190012.

Cf. A085548, A085964, A085965, A085967, A085968, A085969.

Sequence in context: A348807 A204480 A035906 * A239566 A236993 A218513

Adjacent sequences: A190111 A190112 A190113 * A190115 A190116 A190117

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2011

Status

approved