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A055457 5^a(n) exactly divides 5n. Or, 5-adic valuation of 5n. 8
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 October 19 15:49 EDT 2018. Contains 316365 sequences. (Running on oeis4.)