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A051724 Numerator of n/12. 6
0, 1, 1, 1, 1, 5, 1, 7, 2, 3, 5, 11, 1, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2, 25, 13, 9, 7, 29, 5, 31, 8, 11, 17, 35, 3, 37, 19, 13, 10, 41, 7, 43, 11, 15, 23, 47, 4, 49, 25, 17, 13, 53, 9, 55, 14, 19, 29, 59, 5, 61, 31, 21, 16, 65, 11, 67, 17, 23, 35, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Or, numerator of n/(n+12).

Multiplicative with a(2^e) = 2^max(0, e-2), a(3^e) = 3^max(0,e-1), a(p^e) = p^e otherwise. - David W. Wilson, Jun 12 2005

Arises in the equal-tempered musical scale - see Goldstein (1977), Table 1. - N. J. A. Sloane, Aug 29 2018

REFERENCES

Goldstein, A. A. "Optimal temperament." SIAM Review 19.3 (1977): 554-562.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 269.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = n/gcd(n, 12). - David W. Wilson, Jun 12 2005

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

a(n) = A109053(n)/12.

Dirichlet g.f.: zeta(s-1)*(1 - 2/3^s - 1/2^s + 2/6^s - 1/4^s + 2/12^s). (End)

MAPLE

seq(numer(n/12), n=0..100); # Nathaniel Johnston, Apr 18 2011

MATHEMATICA

f[n_]:=Numerator[n/(n+12)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011*)

PROG

(Sage) [lcm(n, 12)/12for n in xrange(0, 72)] # Zerinvary Lajos, Jun 09 2009

(MAGMA) [Numerator(n/12): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011

(PARI) a(n) = numerator(n/12); \\ Michel Marcus, Aug 19 2018

CROSSREFS

Cf. A109053. - Zerinvary Lajos, Jun 09 2009

Sequence in context: A319684 A102778 A135544 * A084303 A011508 A195429

Adjacent sequences:  A051721 A051722 A051723 * A051725 A051726 A051727

KEYWORD

nonn,easy,frac,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 17 18:42 EST 2018. Contains 317276 sequences. (Running on oeis4.)