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.

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A061556 a(n) is the least k > 0 such that sigma(k!) >= n*k!.

Original entry on oeis.org

1, 1, 3, 5, 9, 14, 23, 43, 79, 149, 263, 461, 823, 1451, 2549, 4483, 7879, 13859, 24247, 42683, 75037, 131707, 230773, 405401, 710569, 1246379, 2185021, 3831913, 6720059, 11781551, 20657677
Offset: 0

Views

Author

Labos Elemer, May 17 2001

Keywords

Comments

It seems that, for n > 1, a(n+1) < 2*a(n). Does lim_{n -> infinity} a(n+1)/a(n) = 2? - Benoit Cloitre, Aug 18 2002
Smallest number m such that the abundancy-index of m! is at least n.
Floor(sigma(m!)/m!) = n; note that abundancy-index [= sigma(u)/u] here is not necessarily an integer.
It appears that a(n) = A091440(n) for n >= 13. - Daniel Suteu, Sep 03 2019

Examples

			floor(sigma(842!)/842!) = 11 while floor(sigma(843!)/843!) = 12.

Links

Crossrefs

Cf. A000142, A000203, A023199, A062569.

Programs

  • PARI
    a(n)=if(n<0,0,s=1; while(sigma(s!)

Formula

a(n) = Min{w | floor(sigma(w!)/w!) = n}.

Extensions

More terms from David Wasserman, Jun 18 2002
a(1) inserted and a(21)-a(30) added by Daniel Suteu, Sep 03 2019

A110442 Least colossally abundant number c with sigma(c)/c >= n.

Original entry on oeis.org

6, 120, 55440, 367567200, 288807105787200, 1970992304700453905270400, 46015447651610234928592313897306120347488000, 20945137389024582113645213620899991935836129981347124754955196200225728000
Offset: 2

Views

Author

T. D. Noe, Jul 20 2005

Keywords

Comments

See A110443 for the indices of these numbers in A004490. A073751 contains a program for quickly computing colossally abundant numbers.

Links

Crossrefs

Cf. A000203 (sigma), A004490 (colossally abundant numbers), A023199 (least number k such that sigma(k)/k >= n), A073751, A110443.

A327630 a(n) is the least integer k such that sigma(sigma(k)) >= n*k where sigma is A000203, the sum of divisors.

Original entry on oeis.org

1, 2, 6, 6, 24, 24, 24, 60, 120, 480, 540, 1560, 2520, 10920, 27720, 30240, 191520, 360360, 360360, 3243240, 5765760, 28828800, 109549440, 438197760, 766846080, 3834230400, 9081072000, 32974381440, 147516969600, 880887047040, 2802822422400
Offset: 1

Views

Author

Michel Marcus, Oct 07 2019

Keywords

Comments

From Daniel Suteu, Oct 10 2019: (Start)
a(32) <= 14814918518400,
a(33) <= 64464915715200,
a(34) <= 709114072867200,
a(35) <= 9881550651772800,
a(36) <= 76648784785372800,
a(37) <= 2376112328346556800. (End)

Crossrefs

Cf. A000203, A007539, A023199, A098221, A019278.
Cf. A051027, A272930.

Programs

  • PARI
    a(n) = my(k=1); while (sigma(sigma(k))/k < n, k++); k;

Extensions

a(23)-a(29) from Giovanni Resta, Oct 07 2019
a(30)-a(31) from Giovanni Resta, Feb 27 2020

A240074 Index of the first superabundant number k having abundance >= n.

Original entry on oeis.org

1, 4, 11, 23, 43, 82, 149, 278, 471, 853, 1378, 2594, 4474, 7999, 15747, 27458, 48615, 84320, 166806, 297146, 544525, 973799
Offset: 1

Views

Author

T. D. Noe, Apr 09 2014

Keywords

Comments

Sequence A004394 has a link to a file containing the first 10^6 superabundant numbers. Sequence A023199 lists the first 9 numbers.

Crossrefs

Cf. A004394 (superabundant numbers), A023199.

Formula

a(n) = least k such that A004394(k) > n*k.
Previous Showing 21-24 of 24 results.

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

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