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 A054895 a(n) = Sum_{k>0} floor(n/6^k). 12
 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Different from the highest power of 6 dividing n! (cf. A054861). - Hieronymus Fischer, Aug 14 2007 Partial sums of A122841. - Hieronymus Fischer, Jun 06 2012 LINKS Hieronymus Fischer, Table of n, a(n) for n = 0..10000 FORMULA floor[n/6] + floor[n/36] + floor[n/216] + floor[n/1296] + .... a(n) = (n-A053827(n))/5. From Hieronymus Fischer, Aug 14 2007: (Start) Recurrence: a(n) = floor(n/6) + a(floor(n/6)); a(6*n) = n + a(n); a(n*6^m) = n*(6^m-1)/5 + a(n). a(k*6^m) = k*(6^m-1)/5, for 0<=k<6, m>=0. Asymptotic behavior: a(n) = (n/5) + O(log(n)); a(n+1) - a(n) = O(log(n)); this follows from the inequalities below. a(n) <= (n-1)/5; equality holds for powers of 6. a(n) >= ((n-5)/5) - floor(log_6(n)); equality holds for n=6^m-1, m>0. lim inf (n/5 - a(n)) = 1/5, for n-->oo. lim sup (n/5 - log_6(n) - a(n)) = 0, for n-->oo. lim sup (a(n+1) - a(n) - log_6(n)) = 0, for n-->oo. G.f.: g(x) = sum{k>0, x^(6^k)/(1-x^(6^k))}/(1-x). (End) EXAMPLE a(100)=18. a(10^3)=197. a(10^4)=1997. a(10^5)=19996. a(10^6)=199995. a(10^7)=1999995. a(10^8)=19999994. a(10^9)=199999993. MATHEMATICA Table[t = 0; p = 6; While[s = Floor[n/p]; t = t + s; s > 0, p *= 6]; t, {n, 0, 100} ] PROG (Haskell) a054895 n = a054895_list !! n a054895_list = scanl (+) 0 a122841_list -- Reinhard Zumkeller, Nov 10 2013 CROSSREFS Cf. A011371 and A054861 for analogs involving powers of 2 and 3. Cf. A054861, A054899, A067080, A098844, A122841, A132030. Sequence in context: A097992 A195177 A147583 * A194699 A262694 A137588 Adjacent sequences:  A054892 A054893 A054894 * A054896 A054897 A054898 KEYWORD nonn AUTHOR Henry Bottomley, May 23 2000 EXTENSIONS An incorrect formula was deleted by N. J. A. Sloane, Nov 18 2008 Examples added by Hieronymus Fischer, Jun 06 2012 STATUS approved

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Last modified February 26 11:03 EST 2020. Contains 332279 sequences. (Running on oeis4.)