A190111 Numbers with prime factorization p*q*r*s^2*t^3 (where p, q, r, s, t are distinct primes).

27720, 32760, 41580, 42840, 46200, 47880, 49140, 51480, 54600, 57960, 64260, 64680, 67320, 71400, 71820, 72072, 73080, 75240, 76440, 77220, 78120, 79560, 79800, 85800, 86940, 88920, 91080, 93240, 94248, 96600, 99960, 100980, 101640, 103320

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

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*7*11 = 27720;
a(2) = (2^3)*(3^2)*5*7*13 = 32760;
a(3) = (2^2)*(3^3)*5*7*11 = 41580;
a(4) = (2^3)*(3^2)*5*7*17 = 42840;
a(5) = (2^3)*3*(5^2)*7*11 = 46200.
(End)

Mathematica

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

Prog

(PARI) list(lim)=my(v=List(), t1, t2, t3, t4); forprime(p=2, sqrtnint(lim\420, 3), t1=p^3; forprime(q=2, sqrtint(lim\(30*t1)), if(q==p, next); t2=q^2*t1; forprime(r=2, lim\(6*t2), if(r==p || r==q, next); t3=r*t2; forprime(s=2, lim\(2*t3), if(s==p || s==q || s==r, next); t4=s*t3; forprime(t=2, lim\t4, if(t==p || t==q || t==r || t==s, next); listput(v, t4*t)))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016

Crossrefs

Cf. A179645, A189990, A190109, A190110.

Sequence in context: A230608 A204831 A345153 * A068404 A279091 A307114

Adjacent sequences: A190108 A190109 A190110 * A190112 A190113 A190114

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2011

Status

approved