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A122841 Greatest k such that 6^k divides n.

%I A122841 #39 Jul 23 2022 19:27:12
%S A122841 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%T A122841 0,2,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,
%U A122841 0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0
%N A122841 Greatest k such that 6^k divides n.
%C A122841 See A054895 for the partial sums. - _Hieronymus Fischer_, Jun 08 2012
%H A122841 Reinhard Zumkeller, <a href="/A122841/b122841.txt">Table of n, a(n) for n = 1..10000</a>
%F A122841 From _Hieronymus Fischer_, Jun 03 2012: (Start)
%F A122841 With m = floor(log_6(n)), frac(x) = x-floor(x):
%F A122841 a(n) = Sum_{j=1..m} (1 - ceiling(frac(n/6^j))).
%F A122841 a(n) = m + Sum_{j=1..m} (floor(-frac(n/6^j))).
%F A122841 a(n) = A054895(n) - A054895(n-1).
%F A122841 G.f.: Sum_{j>0} x^6^j/(1-x^6^j). (End)
%F A122841 a(A047253(n)) = 0; a(A008588(n)) > 0; a(A044102(n)) > 1. - _Reinhard Zumkeller_, Nov 10 2013
%F A122841 6^a(n) = A234959(n), n >= 1. - _Wolfdieter Lang_, Jun 30 2014
%F A122841 Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/5. - _Amiram Eldar_, Jan 17 2022
%F A122841 a(n) = min(A007814(n), A007949(n)). - _Jianing Song_, Jul 23 2022
%t A122841 Table[IntegerExponent[n, 6], {n, 1, 100}] (* _Amiram Eldar_, Sep 14 2020 *)
%o A122841 (Haskell)
%o A122841 a122841 = f 0 where
%o A122841    f y x = if r > 0 then y else f (y + 1) x'
%o A122841            where (x', r) = divMod x 6
%o A122841 -- _Reinhard Zumkeller_, Nov 10 2013
%o A122841 (PARI) a(n) = valuation(n, 6); \\ _Michel Marcus_, Jan 17 2022
%Y A122841 Cf. A122840, A007814, A007949, A054895, A234959.
%K A122841 nonn
%O A122841 1,36
%A A122841 _Reinhard Zumkeller_, Sep 13 2006