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 1-3 of 3 results.

A111399 Numbers in A048945 but not in A111398.

Original entry on oeis.org

120, 168, 210, 216, 256, 264, 270, 280, 312, 330, 360, 378, 384, 390, 408, 420, 440, 456, 462, 480, 504, 510, 520, 540, 546, 552, 570, 594, 600, 616, 630, 640, 660, 672, 680, 690, 696, 702, 714, 728, 744, 750, 756, 760, 770, 780, 792, 798, 840
Offset: 1

Views

Author

Ant King, Nov 11 2005

Keywords

Links

Crossrefs

Cf. A048945, A111398.

Programs

  • Mathematica
    q[n_] := Module[{e = FactorInteger[n][[;; , 2]], prod}, (prod = Times @@ (e + 1)) != 8 && Divisible[prod * GCD @@ e, 8] ]; Select[Range[840], q] (* Amiram Eldar, Jan 02 2021 *)
  • PARI
    isok(n) = {prd = 1; fordiv(n, d, prd = prd*d); ispower(prd, 4) && (prd != n^4);}  \\ Michel Marcus, Oct 04 2013

Extensions

More terms from Michel Marcus, Oct 04 2013

A003680 Smallest number with 2n divisors.

Original entry on oeis.org

2, 6, 12, 24, 48, 60, 192, 120, 180, 240, 3072, 360, 12288, 960, 720, 840, 196608, 1260, 786432, 1680, 2880, 15360, 12582912, 2520, 6480, 61440, 6300, 6720, 805306368, 5040, 3221225472, 7560, 46080, 983040, 25920, 10080, 206158430208, 3932160, 184320, 15120
Offset: 1

Views

Author

N. J. A. Sloane, Mira Bernstein

Keywords

Comments

Refers to the least number which is multiplicatively n-perfect, i.e. least number m the product of whose divisors equals m^n. - Lekraj Beedassy, Sep 18 2004
For n=1 to 5, a(n) equals second term of A008578, A007422, A162947, A048945, A030628. - Michel Marcus, Feb 04 2014

References

  • M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
  • A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 23.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005179 (n), A061283 (2n-1), A118224 (at least 2n).

Programs

  • Mathematica
    A005179 = Cases[Import["https://oeis.org/A005179/b005179.txt", "Table"], {, }][[All, 2]];
A = {#, DivisorSigma[0, #]}& /@ A005179;
a[n_] := SelectFirst[A, #[[2]] == 2n&][[1]];
a /@ Range[1000] (* Jean-François Alcover, Nov 10 2019 *)
mp[1, m_] := {{}}; mp[n_, 1] := {{}}; mp[n_?PrimeQ, m_] := If[m < n, {}, {{n}}]; mp[n_, m_] := Join @@ Table[Map[Prepend[#, d] &, mp[n/d, d]], {d, Select[Rest[Divisors[n]], # <= m &]}]; mp[n_] := mp[n, n]; Table[mulpar = mp[2*n] - 1; Min[Table[Product[Prime[s]^mulpar[[j, s]], {s, 1, Length[mulpar[[j]]]}], {j, 1, Length[mulpar]}]], {n, 1, 100}] (* Vaclav Kotesovec, Apr 04 2021 *)
With[{tbl=Table[{n,DivisorSigma[0,n]},{n,800000}]},Table[SelectFirst[tbl,#[[2]]==2k&],{k,20}]][[;;,1]] (* The program generates the first 20 terms of the sequence. *) (* Harvey P. Dale, Jul 06 2025 *)
  • PARI
    a(n)=my(k=2*n); while(numdiv(k)!=2*n, k++); k \\ Charles R Greathouse IV, Jun 23 2017
  • Python
    from sympy import divisors
def a(n):
  m = 4*n - 2
  while len(divisors(m)) != 2*n: m += 1
  return m
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Feb 06 2021

Formula

Bisection of A005179(n). - Lekraj Beedassy, Sep 21 2004

Extensions

More terms from Jud McCranie Oct 15 1997

A111398 Numbers which are the cube roots of the product of their proper divisors.

Original entry on oeis.org

1, 24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 130, 135, 136, 138, 152, 154, 165, 170, 174, 182, 184, 186, 189, 190, 195, 222, 230, 231, 232, 238, 246, 248, 250, 255, 258, 266, 273, 282, 285, 286, 290, 296, 297
Offset: 1

Views

Author

Ant King, Nov 11 2005

Keywords

Comments

This sequence is actually the sequence of 4-multiplicatively perfect numbers all of whose elements (>1) have prime signature {7}, {1,3} or {1,1,1}.

Links

Crossrefs

Cf. A048945, A111399. Essentially the same as A030626.
Cf. A030626, A007956.

Programs

  • Mathematica
    Select[Range[300],Surd[Times@@Most[Divisors[#]],3]==#&] (* Harvey P. Dale, Nov 16 2015 *)
  • PARI
    isok(n) = {prd = 1; fordiv(n, d, prd = prd*d); prd == n^4;} \\ Michel Marcus, Oct 04 2013

Formula

1 together with numbers with 8 divisors. - Vladeta Jovovic, Nov 12 2005

Extensions

More terms from Michel Marcus, Oct 04 2013
Showing 1-3 of 3 results.

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

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