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A214411
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The maximum exponent k of 7 such that 7^k divides n.
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17
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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
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OFFSET
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1,49
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COMMENTS
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7-adic valuation of n.
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
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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
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EXAMPLE
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n=147 = 3*7*7 is divisible by 7^2, so a(147)=2.
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MAPLE
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seq(padic:-ordp(n, 7), n=1..100); # Robert Israel, Mar 05 2020
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Redjan Shabani, Jul 16 2012
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STATUS
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approved
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