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 A214411 The maximum exponent k of 7 such that 7^k divides n. 17
 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,49 COMMENTS 7-adic valuation of n. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA G.f.: Sum_{k>=1} x^(7^k)/(1-x^(7^k)). See A112765. - Wolfdieter Lang, Jun 18 2014 If n == 0 (mod 7) then a(n) = 1 + a(n/7), otherwise a(n) = 0. - M. F. Hasler, Mar 05 2020 Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/6. - Amiram Eldar, Jan 17 2022 EXAMPLE n=147 = 3*7*7 is divisible by 7^2, so a(147)=2. MAPLE seq(padic:-ordp(n, 7), n=1..100); # Robert Israel, Mar 05 2020 MATHEMATICA mek[n_]:=Module[{k=Ceiling[Log[7, n]]}, While[!Divisible[n, 7^k], k--]; k]; Array[ mek, 140] (* Harvey P. Dale, Mar 27 2017 *) IntegerExponent[Range[150], 7] (* Suggested by Amiram Eldar *) (* Harvey P. Dale, Mar 07 2020 *) PROG (PARI) a(n)=valuation(n, 7) \\ Charles R Greathouse IV, Jul 17 2012 (PARI) A=vector(1000); for(i=1, log(#A+.5)\log(7), forstep(j=7^i, #A, 7^i, A[j]++)); A \\ Charles R Greathouse IV, Jul 17 2012 CROSSREFS Cf. A007814 (2-adic), A007949 (3-adic), A112765 (5-adic), A082784. Sequence in context: A347714 A089807 A089810 * A324179 A216577 A096562 Adjacent sequences:  A214408 A214409 A214410 * A214412 A214413 A214414 KEYWORD nonn,easy AUTHOR Redjan Shabani, Jul 16 2012 STATUS approved

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Last modified July 3 16:27 EDT 2022. Contains 355055 sequences. (Running on oeis4.)