Why sigma(n) seems not so performant for small n?

asked 2016-11-15 05:18:12 -0600

logomath gravatar image

updated 2016-11-15 06:10:17 -0600

When I try to timeit sigma(n):

sage: %timeit

sage: for n in xsrange(1,10000): c=sigma(n)

5 loops, best of 3: 181 ms per loop

but it seems much quicker when you directly sum the divisors

sage: %timeit

sage: def s(n): return sum(divisors(n))

sage: for n in xsrange(1,10000): c=s(n)

5 loops, best of 3: 44.8 ms per loop

The same with sigma(n,k). Why that happens (for relatively small n)?

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Comments

Finding divisors uses pari, and maybe pari has gotten faster recently, making your version faster. Or more specifically, maybe pari has gotten faster at listing divisors than at factoring -- sigma uses the factor function. That's just a guess, though.

John Palmieri gravatar imageJohn Palmieri ( 2016-11-15 13:04:23 -0600 )edit

By the way, as far as I can tell, the code for sigma was last changed in 2007 or so. So it may be time to revisit it.

John Palmieri gravatar imageJohn Palmieri ( 2016-11-15 14:13:16 -0600 )edit

Thank you for your hint

logomath gravatar imagelogomath ( 2016-11-17 11:45:04 -0600 )edit