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Package sage :: Package combinat :: Module sloane_functions :: Class A000005
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Class A000005

source code

                      object --+        
                               |        
structure.sage_object.SageObject --+    
                                   |    
                      SloaneSequence --+
                                       |
                                      A000005
Instance Methods [hide private]
 
__init__(self)
The sequence $tau(n)$, which is the number of divisors of $n$.		 source code
 
_repr_(self)
EXAMPLES:...		 source code
 
_eval(self, n)
EXAMPLES:...		 source code

Inherited from SloaneSequence: __call__, __cmp__, __getitem__, __iter__, list

Inherited from structure.sage_object.SageObject: __hash__, __new__, __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, category, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce__, __reduce_ex__, __setattr__, __str__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self)
(Constructor)

source code  

The sequence $tau(n)$, which is the number of divisors of $n$.

This sequence is also denoted $d(n)$ (also called $\tau(n)$ or
$\sigma_0(n)$), the number of divisors of n.

INPUT:
    n -- positive integer

OUTPUT:

EXAMPLES:
    sage: d = sloane.A000005; d
    The integer sequence tau(n), which is the number of divisors of n.
    sage: d(1)
    1
    sage: d(6)
    4
    sage: d(51)
    4
    sage: d(100)
    9
    sage: d(0)
    Traceback (most recent call last):
    ...
    ValueError: input n (=0) must be a positive integer
    sage: d.list(10)
    [1, 2, 2, 3, 2, 4, 2, 4, 3, 4]

AUTHOR:
    -- Jaap Spies (2006-12-10)
    -- William Stein (2007-01-08)
Overrides: SloaneSequence.__init__

_repr_(self)

source code  

EXAMPLES:
    sage: sloane.A000005._repr_()
    'The integer sequence tau(n), which is the number of divisors of n.'
Overrides: SloaneSequence._repr_

_eval(self, n)

source code  

EXAMPLES:
    sage: sloane.A000005._eval(5)
    2
Overrides: SloaneSequence._eval

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