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A190115 Numbers with prime factorization p^2*q^3*r^4 where p, q, and r are distinct primes. 3
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 (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(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
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 3, 4}; Select[Range[900000], f]
PROG
(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
CROSSREFS
Sequence in context: A216142 A340303 A093770 * A203394 A144716 A123078
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)