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A190109
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Numbers with prime factorization p*q^2*r^2*s^3 (where p, q, r, s are distinct primes).
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5
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12600, 17640, 18900, 19800, 23400, 26460, 29400, 29700, 30600, 31500, 34200, 35100, 38808, 41400, 43560, 45864, 45900, 49500, 51300, 52200, 55800, 58212, 58500, 59976, 60840, 60984, 61740, 62100, 65340, 66150, 66600, 67032, 68796, 72600, 73500, 73800, 76500
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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That is, numbers with prime signature {1,2,2,3}.
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LINKS
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EXAMPLE
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a(1) = (2^3)*(3^2)*(5^2)*7 = 12600;
a(2) = (2^3)*(3^2)*5*(7^2) = 17640;
a(3) = (2^2)*(3^3)*(5^2)*7 = 18900;
a(4) = (2^3)*(3^2)*(5^2)*11 = 19800.
(End)
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MATHEMATICA
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f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 2, 2, 3}; Select[Range[150000], f]
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PROG
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(PARI) list(lim)=my(v=List(), t1, t2, t3); forprime(p=2, sqrtnint(lim\180, 3), t1=p^3; forprime(q=2, sqrtint(lim\(12*t1)), if(q==p, next); t2=q^2*t1; forprime(r=2, sqrtint(lim\(2*t2)), if(r==p || r==q, next); t3=r^2*t2; forprime(s=2, lim\t3, if(s==p || s==q || s==r, next); listput(v, t3*s))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016
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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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