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A060819 a(n) = n / gcd(n,4). 44
1, 1, 3, 1, 5, 3, 7, 2, 9, 5, 11, 3, 13, 7, 15, 4, 17, 9, 19, 5, 21, 11, 23, 6, 25, 13, 27, 7, 29, 15, 31, 8, 33, 17, 35, 9, 37, 19, 39, 10, 41, 21, 43, 11, 45, 23, 47, 12, 49, 25, 51, 13, 53, 27, 55, 14, 57, 29, 59, 15, 61, 31, 63, 16, 65, 33, 67, 17, 69, 35, 71, 18, 73, 37, 75, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = A167192(n+4,4). - Reinhard Zumkeller, Oct 30 2009

a(n) = numerator(Sum_{k=1..n} 1/((k+1)*(k+2))). This summation has a closed form of 1/2 - 1/(n+2) and denominator of A145979(n). - Gary Detlefs, Sep 16 2011

a(n) = n / A109008(n). - Reinhard Zumkeller, Nov 25 2013

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

FORMULA

G.f.: (x^7 + x^6 + 3*x^5 + x^4 + 3*x^3 + x^2 + x)/(1 - x^4)^2.

a(n) = 2*a(n-4) - a(n-8).

a(n) = (n/16)*(11 - 5*(-1)^n - i^n - (-i)^n). - Ralf Stephan, Mar 15 2003

a(2*n+1) = a(4*n+2) = 2*n+1, a(4*n+4) = n+1. - Ralf Stephan, Jun 10 2005

Multiplicative with a(2^e) = 2^max(0, e-2), a(p^e) = p^e, p >= 3. - Mitch Harris, Jun 29 2005

a(n) = A109045(n)/4. Dirichlet g.f.: zeta(s-1)*(1-1/2^s-1/2^(2s)). - R. J. Mathar, Apr 18 2011

a(n+4) - a(n) = A176895(n).  - Paul Curtz, Apr 05 2011

a((2*n-1)*2^p) = ceiling(2^(p-2))*(2*n-1), p >= 0 and n >= 1. - Johannes W. Meijer, Feb 06 2013

a(n) = denominator((2n-4)/n). - Wesley Ivan Hurt, Dec 22 2016

MAPLE

A060819 := n -> numer(1/2-1/(n+2)): seq(A060819(n), n=1..75); # Gary Detlefs, Sep 16 2011

MATHEMATICA

f[n_] := n/GCD[n, 4]; Array[f, 76]

PROG

(Sage) [lcm(n, 4)/4for n in xrange(1, 77)] # Zerinvary Lajos, Jun 07 2009

(PARI) { for (n=1, 1000, write("b060819.txt", n, " ", n / gcd(n, 4)); ) } \\ Harry J. Smith, Jul 12 2009

(Haskell)

a060819 n = n `div` a109008 n  -- Reinhard Zumkeller, Nov 25 2013

(MAGMA) [n/GCD(n, 4): n in [1..20]]; // G. C. Greubel, Sep 19 2018

CROSSREFS

Cf. A026741, A051176, A060791, A060789.

Cf. A061037, A061038, A220466.

Sequence in context: A081432 A318060 A136655 * A318661 A089654 A233526

Adjacent sequences:  A060816 A060817 A060818 * A060820 A060821 A060822

KEYWORD

nonn,easy,mult

AUTHOR

Len Smiley, Apr 30 2001

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)