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.

A067382 Numbers n such that sigma(phi(n))/sigma(n) = 2.

Original entry on oeis.org

13, 71, 89, 203, 305, 319, 667, 1363, 1421, 1525, 1711, 1889, 2407, 2933, 3103, 4609, 4615, 4843, 5191, 6583, 7123, 7625, 7627, 9947, 10063, 10411, 11107, 13543, 13891, 14587, 16327, 17023, 19693, 20851, 23075, 24331, 24721, 25027, 25723
Offset: 1

Views

Author

Dean Hickerson, Jan 20 2002

Keywords

Comments

Sequence is infinite. Contains subsequences like 5^i*61, 5^i*13*71, 7^i*29 ... (see also Farideh Firoozbakht's comment on A033631.) - vim(AT)gmx.li, Nov 03 2006

Links

Crossrefs

Cf. A033631, A066831, A067383, A067384, A067385, A197952.

Programs

  • Mathematica
    For[ n=1, True, n++, If[ DivisorSigma[ 1, EulerPhi[ n ] ]/DivisorSigma[ 1, n ]==2, Print[ n ] ] ]
  • PARI
    is(n)=sigma(eulerphi(n=factor(n)))/sigma(n)==2 \\ Charles R Greathouse IV, Nov 27 2013

A067383 Numbers n such that sigma(phi(n))/sigma(n) = 3.

Original entry on oeis.org

181, 899, 2501, 4687, 10991, 12989, 17653, 25199, 25853, 26549, 26657, 54473, 65941, 68381, 72007, 82777, 96197, 98903, 102719, 116449, 124013, 135907, 150121, 169153, 188917, 193553, 201173, 207461, 219559, 234301, 237961, 239279
Offset: 1

Views

Author

Dean Hickerson, Jan 20 2002

Keywords

Links

Crossrefs

Cf. A033631, A066831, A067382, A067384, A067385, A197952.

Programs

  • Mathematica
    For[ n=1, True, n++, If[ DivisorSigma[ 1, EulerPhi[ n ] ]/DivisorSigma[ 1, n ]==3, Print[ n ] ] ]
Select[Range[250000],DivisorSigma[1,EulerPhi[#]]/DivisorSigma[1,#]==3&] (* Harvey P. Dale, Sep 08 2024 *)
  • PARI
    is(n)=sigma(eulerphi(n=factor(n)))/sigma(n)==3 \\ Charles R Greathouse IV, Nov 27 2013

A067384 Numbers n such that sigma(phi(n))/sigma(n) = 4.

Original entry on oeis.org

121679, 1043909, 2350171, 2918263, 3396103, 3566807, 3688067, 4019467, 4562827, 5963407, 7300697, 7485979, 7853933, 8103301, 8364151, 9237779, 9514213, 9638527, 10531123, 11094619, 11384447, 12721937, 13576267
Offset: 1

Views

Author

Dean Hickerson, Jan 20 2002

Keywords

Comments

Subsequence of A066881. - R. J. Mathar, Sep 30 2008

Links

Crossrefs

Cf. A033631, A066831, A067382, A067383, A067385, A197952.

Programs

  • Mathematica
    For[ n=1, True, n++, If[ DivisorSigma[ 1, EulerPhi[ n ] ]/DivisorSigma[ 1, n ]==4, Print[ n ] ] ]
  • PARI
    is(n)=sigma(phi(n=factor(n)))/sigma(n)==4 \\ Charles R Greathouse IV, Nov 27 2013

A067385 a(n) is smallest x such that sigma(phi(x))/sigma(x) = n.

Original entry on oeis.org

1, 13, 181, 121679, 1033474069
Offset: 1

Views

Author

Dean Hickerson, Jan 20 2002

Keywords

Comments

A023199(6) < a(6) <= 1794819234390989. - Donovan Johnson, Oct 24 2011

Crossrefs

Cf. A023199, A033631, A066831, A067382, A067383, A067384, A197952.

Programs

  • Mathematica
    a[ n_ ] := For[ x=1, True, x++, If[ DivisorSigma[ 1, EulerPhi[ x ] ]/DivisorSigma[ 1, x ]==n, Return[ x ] ] ]

Extensions

a(5) from Vim Wenders, Mar 11 2007
Showing 1-4 of 4 results.

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

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