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A106611 a(n) = numerator of n/(n+10). 3
0, 1, 1, 3, 2, 1, 3, 7, 4, 9, 1, 11, 6, 13, 7, 3, 8, 17, 9, 19, 2, 21, 11, 23, 12, 5, 13, 27, 14, 29, 3, 31, 16, 33, 17, 7, 18, 37, 19, 39, 4, 41, 21, 43, 22, 9, 23, 47, 24, 49, 5, 51, 26, 53, 27, 11, 28, 57, 29, 59, 6, 61, 31, 63, 32, 13, 33, 67, 34, 69, 7, 71, 36, 73, 37, 15, 38, 77, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Multiplicative with a(2^e) = 2^max(0,e-1), a(5^e) = 5^max(0,e-1), a(p^e) = p^e if p = 3 or p >= 7. - R. J. Mathar, Apr 18 2011

A strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n,m >= 1. It follows that a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, Feb 17 2019

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..5000

Wikipedia, Quasi-polynomial

FORMULA

From R. J. Mathar, Apr 18 2011: (Start)

a(n) = A109051(n)/10.

Dirichlet g.f.: zeta(s-1)*(1 - 4/5^s - 1/2^s + 4/10^s). (End)

From Peter Bala, Feb 17 2019: (Start)

a(n) = numerator(n/((n + 2)*(n + 5))).

a(n) = n/b(n), where b(n) = [1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, ...] is a purely periodic sequence of period 10. Thus a(n) is a quasi-polynomial in n.

If gcd(n,m) = 1 then a( a(n)*a(m) ) = a(a(n)) * a(a(m)), a( a(a(n))*a(a(m)) ) = a(a(a(n))) * a(a(a(m))) and so on.

O.g.f.: Sum_{d divides 10} A023900(d)*x^d/(1 - x^d)^2 = x/(1 - x)^2 - x^2/(1 - x^2)^2 - 4*x^5/(1 - x^5)^2 + 4*x^10/(1 - x^10)^2.

(End)

MATHEMATICA

f[n_]:=Numerator[n/(n+10)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)

PROG

(Sage) [lcm(n, 10)/10 for n in xrange(0, 79)] # Zerinvary Lajos, Jun 07 2009

(MAGMA) [Numerator(n/(n+10)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011

(GAP) List([0..80], n->NumeratorRat(n/(n+10))); # Muniru A Asiru, Feb 18 2019

CROSSREFS

Cf. A023900. Sequences given by the formula numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060791 (k = 5), A060789 (k = 6), A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20). Cf. A303367.

Sequence in context: A257556 A078268 A124782 * A025261 A111572 A046900

Adjacent sequences:  A106608 A106609 A106610 * A106612 A106613 A106614

KEYWORD

nonn,frac,mult

AUTHOR

N. J. A. Sloane, May 15 2005

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)