A190471 Numbers with prime factorization p^2*q^4*r^4 where p, q, and r are distinct primes.
32400, 63504, 90000, 156816, 202500, 219024, 345744, 374544, 467856, 490000, 685584, 777924, 960400, 1089936, 1210000, 1245456, 1690000, 1774224, 2108304, 2178576, 2396304, 2480625, 2862864, 2890000, 3610000, 3640464, 4112784, 4511376
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]]=={2,4,4}; Select[Range[3500000],f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^2*Prime[n]^4*Prime[m]^4]], {n,33}, {m,33}, {k,33}]; Take[Union@lst,60] -
PARI
list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\4)^(1/8), t1=p^4;forprime(q=p+1, (lim\t1)^(1/4), t2=t1*q^4;forprime(r=2, sqrt(lim\t2), if(p==r||q==r, next);listput(v,t2*r^2)))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016
Formula
Sum_{n>=1} 1/a(n) = P(2)*P(4)^2/2 - P(2)*P(8)/2 - P(4)*P(6) + P(10) = 0.00010139253539568059065..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024