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A190115
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Numbers with prime factorization p^2*q^3*r^4 where p, q, and r are distinct primes.
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3
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10800, 16200, 18000, 21168, 31752, 40500, 45000, 49392, 52272, 67500, 73008, 78408, 98000, 109512, 111132, 124848, 137200, 155952, 172872, 187272, 191664, 228528, 233928, 242000, 245000, 259308, 316368, 338000, 342792, 363312, 415152
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OFFSET
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1,1
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = P(2)*P(3)*P(4) - P(2)*P(7) - P(3)*P(6) - P(4)*P(5) + 2*P(9) = 0.00061171477910848082277..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024
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MATHEMATICA
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f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 3, 4}; Select[Range[900000], f]
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PROG
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(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\72)^(1/4), t1=p^4; 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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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