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 A055457 5^a(n) exactly divides 5n. Or, 5-adic valuation of 5n. 9
 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS More generally, consider the sequence defined by p^a(n) exactly divides p*n. For p = 3 we have A051064 and for p = 2 we have A001511. LINKS T. D. Noe, Table of n, a(n) for n=1..1000 FORMULA G.f.: Sum_{k>=0} x^(5^k)/(1-x^5^k). - Ralf Stephan, Apr 12 2002 Multiplicative with a(p^e) = e+1 if p = 5, 1 otherwise. a(n) = -Sum_{d|n} mu(5d)*tau(n/d). - Benoit Cloitre, Jun 21 2007 Dirichlet g.f.: zeta(s)/(1-1/5^s). - R. J. Mathar, Feb 09 2011 a(n) = A112765(5n). - R. J. Mathar, Jul 17 2012 a(5n) = 1 + a(n).  a(5n+k) = 1 for k = 1..4. - Robert Israel, Dec 07 2015 G.f. satisfies A(x^5) = A(x) - x/(1-x). - Robert Israel, Dec 08 2015 EXAMPLE a(5) = 2 since 5^2 exactly divides 5 times 5; a(25) = 3 since 5^3 exactly divides 5 times 25; a(125) = 4 since 5^4 exactly divides 5 times 125. MAPLE seq(padic:-ordp(5*n, 5), n=1..1000); # Robert Israel, Dec 07 2015 MATHEMATICA max = 1000; s = (1/x)*Sum[x^(5^k)/(1-x^5^k), {k, 0, Log[5, max] // Ceiling }] + O[x]^max; CoefficientList[s, x] (* Jean-François Alcover, Dec 04 2015 *) PROG (PARI) a(n)=-sumdiv(n, d, moebius(5*d)*numdiv(n/d)) \\ Benoit Cloitre, Jun 21 2007 (PARI) a(n)=valuation(5*n, 5) \\ Anders Hellström, Dec 04 2015 CROSSREFS Cf. A001511, A007949, A051064, A112765. Sequence in context: A140345 A177706 A130782 * A277873 A032542 A107038 Adjacent sequences:  A055454 A055455 A055456 * A055458 A055459 A055460 KEYWORD nonn,mult AUTHOR Alford Arnold, Jun 25 2000 STATUS approved

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Last modified July 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)