r"""
Python module for OEIS sequence number A008336.

a(n+1) = a(n)/n if n|a(n) else a(n)*n.

Examples of use.
-----------------------------------------------------------------------
>>> from a008336 import *
>>> print a008336_list(12)
[1, 1, 2, 6, 24, 120, 20, 140, 1120, 10080, 1008, 11088]
>>> print a008336_offset
1
>>> for x in a008336_list_pairs(6):
...     print x
...
(1, 1)
(2, 1)
(3, 2)
(4, 6)
(5, 24)
(6, 120)
>>> print a008336(5)
24
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a008336_offset', 'a008336_list', 'a008336_list_pairs', 'a008336', 'a008336_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a008336_offset = offset = 1

def a008336_gen():
    """Generator function for OEIS sequence A008336."""
    x = 1
    for m in count(1):
        yield x
        x = x/m if x%m == 0 else x*m

def a008336_list(n):
    """Returns a list of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(islice(a008336_gen(), n))

def a008336_list_pairs(n):
    """Returns a list of tuples (n, a(n)) of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(izip(xrange(offset, n+offset), a008336_gen()))

def a008336(n):
    """Returns the term with index n >= 1; offset 1."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a008336_gen(), n-offset, n-offset+1)).pop()