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.

A088833 Numbers n whose abundance is 8: sigma(n) - 2n = 8.

Original entry on oeis.org

56, 368, 836, 11096, 17816, 45356, 77744, 91388, 128768, 254012, 388076, 2087936, 2291936, 13174976, 29465852, 35021696, 45335936, 120888092, 260378492, 381236216, 775397948, 3381872252, 4856970752, 6800228816, 8589344768, 44257207676, 114141404156
Offset: 1

Views

Author

Labos Elemer, Oct 28 2003

Keywords

Comments

A subset of A045770.
If p=2^m-9 is prime (m is in the sequence A059610) then n=2^(m-1)*p is in the sequence. See comment lines of the sequence A088831. 56, 368, 128768, 2087936 & 8589344768 are of the mentioned form. - Farideh Firoozbakht, Feb 15 2008
a(28) > 10^12. - Donovan Johnson, Dec 08 2011
a(31) > 10^13. - Giovanni Resta, Mar 29 2013
a(38) > 10^18. - Hiroaki Yamanouchi, Aug 23 2018
Any term x of this sequence can be combined with any term y of A125247 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016

Examples

			Except first 4 terms of A045770 (1, 7, 10, and 49) are here: abundances = {-1,-6,-2,-41,8,8,8,8,8,8,8,8,8,8,8,8,8}.

Links

Crossrefs

Cf. A033880, A045668, A045669, A045770, A088831, A088832, A059610, A125247 (deficiency 8).

Programs

Extensions

a(14)-a(17) from Farideh Firoozbakht, Feb 15 2008
a(18)-a(25) from Donovan Johnson, Dec 23 2008
a(26)-a(27) from Donovan Johnson, Dec 08 2011

A045687 Number of 2n-bead balanced binary necklaces of fundamental period 2n which are equivalent to their reversed complement, but are not equivalent to their reverse and complement.

Original entry on oeis.org

0, 0, 0, 2, 4, 12, 24, 56, 112, 238, 480, 992, 1980, 4032, 8064, 16242, 32512, 65280, 130536, 261632, 523260, 1047494, 2095104, 4192256, 8384400, 16773108, 33546240, 67100432, 134201340, 268419072, 536837640, 1073709056, 2147418112
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

The number of length 2n balanced binary Lyndon words which are equivalent to their reversed complement is A000740(n) and the number which are equivalent to their reverse, complement and reversed complement is A045683(n). - Andrew Howroyd, Sep 28 2017

Links

Crossrefs

Cf. A000740, A045669, A045678, A045683.

Programs

  • Mathematica
    a740[n_] := DivisorSum[n, MoebiusMu[n/#]*2^(#-1)&];
a45674[0] = 1; a45674[n_] := Module[{t = 0, r = n}, While[EvenQ[r], r = Quotient[r, 2]; t += 2^(r-1)]; t + 2^Quotient[r, 2]];
a45683[0] = 1; a45683[n_] := DivisorSum[n, MoebiusMu[n/#]*a45674[#]&];
a[0] = 0; a[n_] := a740[n] - a45683[n];
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Sep 30 2017, after Andrew Howroyd *)

Formula

From Andrew Howroyd, Sep 28 2017: (Start)
Moebius transform of A045678.
a(n) = A000740(n) - A045683(n).
(End)

Extensions

Incorrect formulas and comments removed by Andrew Howroyd, Sep 28 2017

A045660 Number of 2n-bead balanced binary strings, rotationally equivalent to reversed complement, inequivalent to reverse and complement.

Original entry on oeis.org

0, 0, 0, 12, 32, 120, 300, 784, 1824, 4296, 9720, 21824, 47852, 104832, 226576, 487392, 1042208, 2219520, 4703880, 9942016, 20940152, 43995544, 92206400, 192843776, 402500844, 838655520, 1744509312, 3623427624, 7515501648
Offset: 0

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A045655, A045656, A045669.

Formula

From Andrew Howroyd, Sep 15 2019: (Start)
Inverse Moebius transform of A045669.
a(n) = A045655(n) - A045656(n). (End)
Showing 1-3 of 3 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.