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.

A213594 Greatest number k such that A048784(n) / 2^k is an integer.

Original entry on oeis.org

1, 2, 1, 3, 1, 3, 5, 4, 4, 4, 7, 5, 6, 7, 5, 7, 8, 7, 9, 8, 11, 11, 8, 7, 9, 11, 8, 13, 12, 11, 12, 11, 12, 12, 14, 13, 15, 15, 11, 13, 14, 18, 15, 15, 15, 14, 17, 14, 17, 18, 18, 20, 17, 19, 19, 19, 18, 19, 21, 19, 19, 21, 20, 22, 18, 21, 24, 22, 26, 24, 20
Offset: 1

Views

Author

Michel Lagneau, Jun 15 2012

Keywords

Comments

2-adic valuation of A048784.
Property: a(n) > 0, that is A048784(n) is even, for n > 0.

Examples

			a(7) = 5 because A048784(7) / 2^5 = 32 / 32 = 1 is an integer.

Links

Crossrefs

Cf. A000005, A048784.

Programs

  • Maple
    with(numtheory): for n from 1 to 100 do:ii:=0:for k from 500 by -1 to 1 while(ii=0) do: x:=evalf(tau(binomial(2*n,n))/2^k):if x=floor(x) then ii:=1: printf(`%d, `,k):else fi:od:od:
  • PARI
    a(n)=valuation(numdiv(binomial(2*n,n)),2) \\ Charles R Greathouse IV, Jun 15 2012

A228378 Numbers n such that tb(n) = tb(n+1) where tb(n) = A048784(n) is the number of divisors of binomial(2*n, n).

Original entry on oeis.org

9, 10, 22, 34, 44, 45, 51, 56, 82, 106, 130, 141, 142, 162, 166, 177, 185, 190, 230, 262, 273, 274, 320, 322, 346, 352, 354, 394, 440, 454, 470, 526, 536, 550, 562, 586, 606, 624, 635, 670, 692, 717, 754, 766, 779, 814, 826, 831, 862, 882, 891, 920, 934
Offset: 1

Views

Author

Michel Marcus, Aug 21 2013

Keywords

Links

Crossrefs

Cf. A000005, A000984.

Programs

  • Mathematica
    SequencePosition[Table[DivisorSigma[0,Binomial[2n,n]],{n,1000}],{x_,x_}][[All,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 15 2019 *)
  • PARI
    lista(nn) = my(last = 0); for (i=1, nn, new = numdiv(binomial(2*i,i)); if (last == new, print1(i, ", ")); last = new) \\ Michel Marcus, Aug 21 2013

A213595 a(n) = A048784(n) / 2^A213594(n).

Original entry on oeis.org

1, 1, 3, 1, 9, 3, 1, 3, 3, 3, 1, 3, 3, 3, 15, 3, 3, 9, 3, 9, 1, 1, 15, 27, 9, 3, 15, 1, 5, 5, 3, 9, 9, 9, 3, 3, 1, 3, 45, 9, 15, 1, 15, 15, 15, 45, 9, 81, 9, 5, 5, 1, 25, 5, 3, 3, 5, 5, 3, 15, 27, 9, 21, 3, 81, 9, 3, 15, 1, 3, 75, 81, 9, 9, 135, 27, 25, 15
Offset: 1

Views

Author

Michel Lagneau, Jun 15 2012

Keywords

Comments

a(n) = tau(binomial(2*n,n)) / 2^k, where tau = number of divisors (A000005) and k is the greatest possible integer.

Examples

			a(7) = 1 because A048784(7) / 2^5 = 32 / 32 = 1 is an integer.

Crossrefs

Cf. A048784, A213594.

Programs

  • Maple
    with(numtheory): for n from 1 to 100 do:ii:=0:for k from 500 by -1 to 1 while(ii=0) do: x:=evalf(tau(binomial(2*n,n))/2^k):if x=floor(x) then ii:=1: printf(`%d, `,floor(x)):else fi:od:od:

A067819 Sum of the divisors of binomial(2n,n).

Original entry on oeis.org

3, 12, 42, 144, 728, 2688, 10080, 39312, 127008, 423360, 2419200, 6773760, 32140800, 160704000, 626745600, 1940889600, 9289728000, 38397542400, 156332851200, 642477588480, 2223960883200, 8154523238400, 36280077926400
Offset: 1

Views

Author

Joseph L. Pe, Feb 08 2002

Keywords

Links

Crossrefs

Cf. A000203, A000984, A048784.

Programs

  • Mathematica
    Table[DivisorSigma[1, Binomial[2 n, n]], {n, 30}]
  • PARI
    a(n) = sigma(binomial(2*n,n)); \\ Michel Marcus, Sep 28 2019

Formula

a(n) = A000203(A000984(n)). - Amiram Eldar, Sep 28 2019
Showing 1-4 of 4 results.

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

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