A190109 Numbers with prime factorization p*q^2*r^2*s^3 (where p, q, r, s are distinct primes).

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

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