A190114 - OEIS

%I #17 Mar 07 2024 01:29:51

%S 7200,14112,24300,34848,39200,47628,48672,83232,96800,103968,112500,

%T 117612,135200,152352,164268,189728,231200,242208,264992,276768,

%U 280908,288800,297675,350892,394272,423200,453152,484128,514188,532512,566048

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

%H T. D. Noe, <a href="/A190114/b190114.txt">Table of n, a(n) for n = 1..1000</a>

%H Will Nicholes, <a href="https://willnicholes.com/2010/06/06/list-of-prime-signatures">List of prime signatures</a>, 2010.

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>.

%F 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

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,2,5};Select[Range[900000],f]

%t 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 *)

%o (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

%Y Cf. A179665, A190011, A190012.

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

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 04 2011