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A190109 Numbers with prime factorization p*q^2*r^2*s^3 (where p, q, r, s are distinct primes). 4
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 October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)