A190470 Numbers with prime factorization p^2*q^3*r^5 where p, q, and r are distinct primes.
21600, 36000, 42336, 48600, 95256, 98784, 104544, 121500, 146016, 196000, 225000, 235224, 249696, 274400, 311904, 328536, 333396, 337500, 383328, 457056, 484000, 561816, 632736, 676000, 701784, 726624, 830304, 1028376, 1064800, 1156000
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]]=={2,3,5}; Select[Range[2500000],f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^2*Prime[n]^3*Prime[m]^5]], {n,20}, {m,20}, {k,20}]; Take[Union@lst,60] -
PARI
list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\72)^(1/5), t1=p^5;forprime(q=2, (lim\t1)^(1/3), if(p==q, next);t2=t1*q^3;forprime(r=2, sqrt(lim\t2), if(p==r||q==r, next);listput(v,t2*r^2)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011
Formula
Sum_{n>=1} 1/a(n) = P(2)*P(3)*P(5) - P(2)*P(8) - P(3)*P(7) - P(5)^2 + 2*P(10) = 0.00025025315357155375895..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024