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A190470 Numbers with prime factorization p^2*q^3*r^5 where p, q, and r are distinct primes. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Will Nicholes, List of prime signatures, 2010.
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
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]
PROG
(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
CROSSREFS
Sequence in context: A252393 A211236 A221002 * A113620 A074812 A037160
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)