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 A190109 Numbers with prime factorization p*q^2*r^2*s^3 (where p, q, r, s are distinct primes). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS That is, numbers with prime signature {1,2,2,3}. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Prime signature. Wikipedia, Prime signature. Will Nicholes, Prime Signatures. Index to sequences related to prime signature EXAMPLE From Petros Hadjicostas, Oct 26 2019: (Start) 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) MATHEMATICA f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 2, 2, 3}; Select[Range[150000], f] PROG (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 CROSSREFS Cf. A190106, A190107, A190108. Sequence in context: A235103 A216990 A237086 * A272516 A246231 A248709 Adjacent sequences: A190106 A190107 A190108 * A190110 A190111 A190112 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, May 04 2011 STATUS approved

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Last modified May 28 19:55 EDT 2024. Contains 372919 sequences. (Running on oeis4.)