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
Keywords
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.
Programs
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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 *) -
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
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