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 A060904 Largest power of 5 that divides n. 16
 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Also the largest power of 5 that divides the n-th Fibonacci number A000045(n). Multiplicative with a(p^e) = 5^e if p = 5, else a(p^e) = 1. - Mitch Harris, Apr 19 2005 Also 5-adic value of 1/n, n >= 1. See the Mahler reference, definition on p. 7. This is a non-archimedean valuation. See Mahler, p. 10. Sometimes also called 5-adic absolute value. - Wolfdieter Lang, Jun 30 2014 REFERENCES K. Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143. FORMULA If n is not divisible by 5, then a(n) = 1. If n = 5^k * m where m is not divisible by 5, then a(n) = 5^k. Dirichlet g.f.: zeta(s)*(5^s-1)/(5^s-5). - R. J. Mathar, Jul 12 2012 a(n) = 5^A112765(n). - Tom Edgar, Mar 22 2014 From Peter Bala, Feb 21 2019: (Start) a(n) = gcd(n,5^n). a(n) = n/A132739(n). O.g.f.: x/(1 - x) + 4*Sum_{n >= 1} 5^(n-1)*x^(5^n)/ (1 - x^(5^n)). (End). a(n) = (1/5)*(sigma(5*n) - sigma(n))/(sigma(5*n) - 5*sigma(n)), where sigma(n) = A000203(n). - Peter Bala, Jun 10 2022 EXAMPLE a(10) = 5 because 10 = 5 * 2. MAPLE A060904 := n -> 5^padic[ordp](n, 5): # Peter Luschny, Nov 26 2010 MATHEMATICA Table[5^IntegerExponent[n, 5], {n, 100}] (* Vincenzo Librandi, Dec 29 2015 *) PROG (Sage) [5^valuation(i, 5) for i in [1..100]] # Tom Edgar, Mar 22 2014 (PARI) a(n)=5^valuation(n, 5) \\ Charles R Greathouse IV, Aug 05 2015 (MAGMA) [5^Valuation(n, 5): n in [1..100]]; // Vincenzo Librandi, Dec 29 2015 CROSSREFS Cf. A000045, A000203, A038500, A060865, A060901, A132739, A268354, A268357. Sequence in context: A257461 A129398 A109009 * A351084 A135469 A348735 Adjacent sequences:  A060901 A060902 A060903 * A060905 A060906 A060907 KEYWORD nonn,easy,mult,changed AUTHOR Ahmed Fares (ahmedfares(AT)my-deja.com), May 06 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001 Edited by Joerg Arndt and M. F. Hasler, Dec 29 2015 STATUS approved

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Last modified June 30 12:41 EDT 2022. Contains 354939 sequences. (Running on oeis4.)