This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054896 a(n) = Sum_{k>0} floor(n/7^k). 12
 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,15 COMMENTS Highest power of 7 dividing n!. LINKS Hieronymus Fischer, Table of n, a(n) for n = 0..10000 FORMULA floor[n/7] + floor[n/49] + floor[n/343] + floor[n/2401] + .... a(n) = (n - A053828(n))/6. From Hieronymus Fischer, Aug 14 2007: (Start) Recurrence: a(n) = floor(n/7) + a(floor(n/7)); a(7*n) = n + a(n); a(n*7^m) = n*(7^m-1)/6+a(n). a(k*7^m) = k*(7^m-1)/6, for 0<=k<7, m>=0. Asymptotic behavior: a(n) = n/6 + O(log(n)), a(n+1) - a(n) = O(log(n)); this follows from the inequalities below. a(n) <= (n-1)/6; equality holds for powers of 7. a(n) >= (n-6)/6 - floor(log_7(n)); equality holds for n=7^m-1, m>0. - lim inf (n/6 - a(n)) = 1/6, for n-->oo. lim sup (n/6 - log_7(n) - a(n)) = 0, for n-->oo. lim sup (a(n+1) - a(n) - log_7(n)) = 0, for n-->oo. G.f.: g(x) = sum{k>0, x^(7^k)/(1-x^(7^k))}/(1-x). (End) EXAMPLE a(100)=16. a(10^3)=164. a(10^4)=1665. a(10^5)=16662. a(10^6)=166664. a(10^7)=1666661. a(10^8)=16666662. a(10^9)=166666661 MATHEMATICA Table[t = 0; p = 7; While[s = Floor[n/p]; t = t + s; s > 0, p *= 7]; t, {n, 0, 100} ] CROSSREFS Cf. A011371 and A054861 for analogs involving powers of 2 and 3. Cf. A054895, A054899, A067080, A098844, A132031. Sequence in context: A132270 A195174 A187185 * A052364 A052374 A003074 Adjacent sequences:  A054893 A054894 A054895 * A054897 A054898 A054899 KEYWORD nonn AUTHOR Henry Bottomley, May 23 2000 EXTENSIONS Examples added by Hieronymus Fischer, Jun 06 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 21 06:11 EDT 2019. Contains 326162 sequences. (Running on oeis4.)