A179695 Numbers of the form p^3*q^2*r^2 where p, q, and r are distinct primes.

1800, 2700, 3528, 4500, 5292, 8712, 9800, 12168, 12348, 13068, 18252, 20808, 24200, 24500, 25992, 31212, 33075, 33800, 34300, 38088, 38988, 47432, 47916, 55125, 57132, 57800, 60500, 60552, 66248, 69192, 72200, 77175, 79092, 81675, 84500

Offset

1,1

Comments

Subsequence of A225228. - Reinhard Zumkeller, May 03 2013

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

A050326(a(n)) = 5. - Reinhard Zumkeller, May 03 2013

Sum_{n>=1} 1/a(n) = P(2)^2*P(3)/2 - P(3)*P(4)/2 - P(2)*P(5) + P(7) = 0.0032578591481263202818..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 3}; Select[Range[10^5], f]
f[n_]:={Times@@(n^{2, 2, 3}), Times@@(n^{2, 3, 2}), Times@@(n^{3, 2, 2})}; Module[ {nn=20}, Select[Flatten[f/@Subsets[Prime[Range[nn]], {3}]], #<= 72*Prime[ nn]^2&]]//Union (* Harvey P. Dale, Jul 05 2019 *)

Prog

(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\36)^(1/3), t1=p^3; 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 24 2011

Crossrefs

Cf. A050326, A225228.

Cf. A085548, A085541, A085964, A085965, A085967.

Sequence in context: A235898 A035891 A069476 * A025139 A035767 A107563

Adjacent sequences: A179692 A179693 A179694 * A179696 A179697 A179698

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 24 2010

Status

approved