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A112765
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Exponent of highest power of 5 dividing n.
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12
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0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1
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OFFSET
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1,25
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COMMENTS
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A027868 gives partial sums.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
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FORMULA
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Totally additive with a(p) = 1 if p = 5, 0 otherwise.
Contribution from Hieronymus Fischer, Jun 8 2012 (Start):
With m = floor(log_5(n)), frac(x) = x-floor(x):
a(n) = sum_{j=1..m} (1 - ceiling(frac(n/5^j))).
a(n) = m + sum_{j=1..m} (floor(-frac(n/5^j))).
a(n)= A027868(n) - A027868(n-1).
G.f.: g(x)= sum_{j>0} x^5^j/(1-x^5^j). (End)
a(5n) = A055457(n). - R. J. Mathar, Jul 17 2012
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PROG
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(Haskell)
a112765 n = fives n 0 where
fives n e | r > 0 = e
| otherwise = fives n' (e + 1) where (n', r) = divMod n 5
-- Reinhard Zumkeller, Apr 08 2011
(Pari) A112765(n)=valuation(n, 5); /* Joerg Arndt, Apr 08 2011 */
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CROSSREFS
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Cf. A007814, A007949, A112762, A022337.
Cf. A122840.
Cf. A027868, A054899, A122841 A160093, A160094, A196563, A196564.
Sequence in context: A073345 A216511 A138088 * A105966 A083915 A083892
Adjacent sequences: A112762 A112763 A112764 * A112766 A112767 A112768
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Sep 18 2005
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STATUS
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approved
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