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 A214411 The maximum exponent k of 7 such that 7^k divides n. 11
 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 Multiplicity of factor 7 in the prime factorization of n; 7-adic valuation of n. The p-adic valuation nu_p(n) (Greek nu in the standard literature) of n for primes p has the property that nu_p(n)=0 if n mod p <>0, nu_p(p)=1, nu_p(0)=0, and nu_p(n) = 1+ nu_p(n-n/p) if nu_p(n-p) <>0. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA If n=7 then a(n)=1; else if a(n-7) <> 0 then a(n) = 1 + a(n-n/7); else a(n)=0. G.f.: sum(x^(7^k)/(1-x^(7^k)), k=1..infinity). See A112765. - Wolfdieter Lang, Jun 18 2014 EXAMPLE For n=147 = 3*7*7, 147 is divisible by 7^2, so a(147)=2. 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 *) PROG (MATLAB) % Input: %  n: an integer % Output: %  m: max power of 7 such that 7^m divides n %  M: 1-by-K matrix where M(i) is the max power of 7 such that 7^M(i) divides n function [m, M] = Omega7(n)   M = NaN*zeros(1, n);   M(1:6)=0; M(7)=1;     for k=8:n       if M(n-7)~=0         M(k)=M(k-k/7)+1;       else         M(k)=0;       end     end     m=M(end); end (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: A280618 A089807 A089810 * A216577 A096562 A096563 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 January 18 21:54 EST 2019. Contains 319282 sequences. (Running on oeis4.)