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A190378 Numbers with prime factorization p*q*r*s*t*u^3 (where p, q, r, s, t, u are distinct primes). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)