A190378 Numbers with prime factorization p*q*r*s*t*u^3 (where p, q, r, s, t, u are distinct primes).

120120, 157080, 175560, 185640, 207480, 212520, 251160, 267960, 270270, 271320, 286440, 291720, 316680, 326040, 328440, 338520, 341880, 353430, 367080, 378840, 394680, 395010, 397320, 404040, 408408, 414120, 417690, 426360, 434280, 442680

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*5*7*11*13 = 120120;
a(2) = (2^3)*3*5*7*11*17 = 157080,
a(3) = (2^3)*3*5*7*11*19 = 175560;
a(4) = (2^3)*3*5*7*13*17 = 185640;
a(5) = (2^3)*3*5*7*13*19 = 207480;
a(6) = (2^3)*3*5*7*11*23 = 212520;
a(7) = (2^3)*3*5*7*13*23 = 251160;
a(8) = (2^3)*3*5*7*11*29 = 267960;
a(9) = 2*(3^3)*5*7*11*13 = 270270.
(End)

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1, 1, 1, 1, 1, 3}; Select[Range[1000000], f]

Prog

(PARI) list(lim)=my(v=List(), t1, t2, t3, t4, t5); forprime(p=2, sqrtnint(lim\2310, 3), t1=p^3; forprime(q=2, lim\(210*t1), if(q==p, next); t2=q*t1; forprime(r=2, lim\(30*t2), if(r==p || r==q, next); t3=r*t2; forprime(s=2, lim\(6*t3), if(s==p || s==q || s==r, next); t4=s*t3; forprime(t=2, lim\(2*t4), if(t==p || t==q || t==r || t==s, next); t5=t*t4; forprime(u=2, lim\t5, if(u==p || u==q || u==r || u==s || u==t, next); listput(v, t5*u))))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016

Crossrefs

Cf. A190110, A190111.

Sequence in context: A236094 A043622 A272597 * A092015 A250673 A278005

Adjacent sequences: A190375 A190376 A190377 * A190379 A190380 A190381

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 09 2011

Extensions

Name edited by Petros Hadjicostas, Oct 26 2019

Status

approved