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 1-2 of 2 results.

A243473 a(n) = numerator(sigma(n)/n) - denominator(sigma(n)/n) where sigma(n) = sum of divisors of n.

Original entry on oeis.org

0, 1, 1, 3, 1, 1, 1, 7, 4, 4, 1, 4, 1, 5, 3, 15, 1, 7, 1, 11, 11, 7, 1, 3, 6, 8, 13, 1, 1, 7, 1, 31, 5, 10, 13, 55, 1, 11, 17, 5, 1, 9, 1, 10, 11, 13, 1, 19, 8, 43, 7, 23, 1, 11, 17, 8, 23, 16, 1, 9, 1, 17, 41, 63, 19, 13, 1, 29, 9, 37, 1, 41, 1, 20, 49, 16
Offset: 1

Views

Author

Michel Marcus, Jun 05 2014

Keywords

Comments

a(n) = 1 for n prime or perfect (A053813).
a(n) = A001065(n) when n is in A014567.
a(n) > n for n in A069057. - Michel Marcus, May 04 2016

Crossrefs

Programs

  • Mathematica
    f[n_] := DivisorSigma[1, n]/n; Table[Numerator[f@ n] - Denominator[f@ n], {n, 76}] (* Michael De Vlieger, Sep 09 2015 *)
  • PARI
    a(n) = numerator(ab = sigma(n)/n) - denominator(ab);

Formula

a(n) = A017665(n) - A017666(n).

A069096 Numbers k such that the numerator of Sum_{d|k} 1/d > 3*k.

Original entry on oeis.org

900, 3600, 8100, 14400, 17424, 22500, 32400, 57600, 69696, 72900, 90000, 108900, 129600, 166464, 202500, 230400, 260100, 278784, 291600, 345744, 360000, 374544, 435600, 476100, 518400, 562500, 656100, 665856, 685584, 756900, 810000, 921600
Offset: 1

Views

Author

Benoit Cloitre, Apr 07 2002

Keywords

Crossrefs

Programs

  • Mathematica
    Select[Range[10^6], Numerator @ DivisorSigma[-1, #] > 3*# &] (* Amiram Eldar, Feb 19 2021 *)
  • PARI
    isok(k) = numerator(sumdiv(k, d, 1/d)) > 3*k; \\ Michel Marcus, Feb 15 2021
Showing 1-2 of 2 results.