A190109 - OEIS

%I #23 Feb 16 2025 08:33:14

%S 12600,17640,18900,19800,23400,26460,29400,29700,30600,31500,34200,

%T 35100,38808,41400,43560,45864,45900,49500,51300,52200,55800,58212,

%U 58500,59976,60840,60984,61740,62100,65340,66150,66600,67032,68796,72600,73500,73800,76500

%N Numbers with prime factorization p*q^2*r^2*s^3 (where p, q, r, s are distinct primes).

%C That is, numbers with prime signature {1,2,2,3}.

%H T. D. Noe, <a href="/A190109/b190109.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSignature.html">Prime signature</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_signature">Prime signature</a>.

%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>.

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>

%e From _Petros Hadjicostas_, Oct 26 2019: (Start)

%e a(1) = (2^3)*(3^2)*(5^2)*7 = 12600;

%e a(2) = (2^3)*(3^2)*5*(7^2) = 17640;

%e a(3) = (2^2)*(3^3)*(5^2)*7 = 18900;

%e a(4) = (2^3)*(3^2)*(5^2)*11 = 19800.

%e (End)

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,2,2,3};Select[Range[150000],f]

%o (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

%Y Cf. A190106, A190107, A190108.

%K nonn,changed

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 04 2011