cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A190383 Numbers with prime factorization pqrst^5.

Original entry on oeis.org

36960, 43680, 57120, 63840, 68640, 77280, 89760, 96096, 97440, 100320, 104160, 106080, 118560, 121440, 124320, 125664, 137760, 140448, 143520, 144480, 148512, 153120, 155040, 157920, 160160, 163680, 165984, 170016, 178080, 180960, 187110
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 09 2011

Keywords

Links

Crossrefs

Cf. A190320, A190382.

Programs

  • Mathematica
    f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,1,5};Select[Range[500000],f]
  • PARI
    list(lim)=my(v=List(),t1,t2,t3,t4); forprime(p1=2,sqrtnint(lim\210, 5), t1=p1^5; forprime(p2=2,lim\(30*t1), if(p2==p1, next); t2=p2*t1; forprime(p3=2,lim\(6*t2), if(p3==p1 || p3==p2, next); t3=p3*t2; forprime(p4=2,lim\(2*t3), if(p4==p1 || p4==p2 || p4==p3, next); t4=p4*t3; forprime(p5=2,lim\t4, if(p5==p1 || p5==p2 || p5==p3 || p5==p4, next); listput(v, t4*p5)))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016

A190384 Numbers with prime factorization pqrs^2t^4.

Original entry on oeis.org

55440, 65520, 85680, 92400, 95760, 102960, 109200, 115920, 124740, 129360, 134640, 142800, 144144, 146160, 147420, 150480, 152880, 156240, 159120, 159600, 171600, 177840, 182160, 186480, 188496, 192780, 193200, 199920, 203280, 206640
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 09 2011

Keywords

Links

Crossrefs

Cf. A190382, A190383.

Programs

  • Mathematica
    f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,2,4};Select[Range[300000],f]
  • PARI
    list(lim)=my(v=List(),t1,t2,t3,t4); forprime(p1=2,sqrtnint(lim\420, 4), t1=p1^4; forprime(p2=2,sqrtint(lim\(30*t1)), if(p2==p1, next); t2=p2^2*t1; forprime(p3=2,lim\(6*t2), if(p3==p1 || p3==p2, next); t3=p3*t2; forprime(p4=2,lim\(2*t3), if(p4==p1 || p4==p2 || p4==p3, next); t4=p4*t3; forprime(p5=2,lim\t4, if(p5==p1 || p5==p2 || p5==p3 || p5==p4, next); listput(v, t4*p5)))))); Set(v) \\ Charles R Greathouse IV, Aug 25 2016

A190385 Numbers with prime factorization pqrs^3t^3.

Original entry on oeis.org

83160, 98280, 128520, 143640, 154440, 173880, 201960, 216216, 219240, 225720, 231000, 234360, 238680, 266760, 273000, 273240, 279720, 282744, 309960, 316008, 322920, 325080, 334152, 344520, 348840, 355320, 357000, 368280, 373464, 382536
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 09 2011

Keywords

Links

Crossrefs

Cf. A190382, A190383, A190384.

Programs

  • Mathematica
    f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,3,3};Select[Range[600000],f]
  • PARI
    list(lim)=my(v=List(),t1,t2,t3,t4); forprime(p=2,sqrtnint(lim\840, 3), t1=p^3; forprime(q=2,sqrtnint(lim\(30*t1), 3), if(q==p, next); t2=q^3*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

A381315 Numbers whose prime factorization exponents include exactly one 3 and no exponent greater than 3.

Original entry on oeis.org

8, 24, 27, 40, 54, 56, 72, 88, 104, 108, 120, 125, 135, 136, 152, 168, 184, 189, 200, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 343, 344, 351, 360, 375, 376, 378, 392, 408, 424, 440, 456, 459, 472, 488, 500, 504, 513, 520, 536, 540, 552, 568, 584, 594
Offset: 1

Views

Author

Amiram Eldar, Feb 19 2025

Keywords

Comments

Subsequence of A176297 and A375072, and first differs from them at n = 20: A176297(20) = A375072(20) = 216 = 2^3 * 3^3 is not a term of this sequence.
The asymptotic density of this sequence is (1/zeta(3)) * Sum_{p prime} 1/(p+p^2+p^3) = 0.089602607198058453295... .

Links

Crossrefs

Subsequence of A046100, A176297, A375072 and A375145.
Subsequences: A030078, A048109, A065036, A143610, A163569, A179670, A179695, A179700, A189975, A189984, A190109, A190378, A190382.
Cf. A002117.

Programs

  • Mathematica
    q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, MemberQ[e, 3] && Count[e, _?(# < 3 &)] == Length[e] - 1]; Select[Range[600], q]
  • PARI
    isok(k) = {my(e = factor(k)[, 2]~); select(x -> x > 2, e) == [3];}
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.