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A164848 a(n) = A026741(n)/A051712(n+1). 1
1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Twice connected to Bernoulli numbers A164555/A027642 via the Akiyama-Tanigawa algorithm.
Conjecture (checked for the first 3000 entries): periodic with a(n+24)=a(n).
Is this a multiplicative function?
Multiplicative because both A026741 and A051712(n+1) are. - Andrew Howroyd, Jul 26 2018
LINKS
FORMULA
a(n) = gcd(12, n/gcd(2, n)). - Andrew Howroyd, Jul 26 2018
From Amiram Eldar, Oct 28 2023: (Start)
Multiplicative with a(2^3) = 2^min(e-1,2), a(3^e) = 3, and a(p^e) = 1 for a prime p >= 5.
Dirichlet g.f.: zeta(s) * (1 + 1/2^(2*s) + 1/2^(3*s-1)) * (1 + 2/3^s).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5/2. (End)
MAPLE
b := proc(n) n/(n+1)/(n+2) ; end: A051712 := proc(n) numer( b(n)-b(n+1)) ; end:
A026741 := proc(n) if type(n, 'odd') then n; else n/2; fi; end:
A164848 := proc(n) A026741(n)/A051712(n+1) ; end: seq(A164848(n), n=1..120) ; # R. J. Mathar, Sep 06 2009
MATHEMATICA
Table[GCD[12, n / GCD[2, n]], {n, 100}] (* Vincenzo Librandi, Jul 26 2018 *)
PROG
(PARI) a(n) = gcd(12, n/gcd(2, n)); \\ Andrew Howroyd, Jul 26 2018
(Magma) [Gcd(12, n div Gcd(2, n)): n in [1..100]]; // Vincenzo Librandi, Jul 26 2018
CROSSREFS
Sequence in context: A205564 A036585 A260454 * A213514 A130827 A070309
KEYWORD
nonn,easy,mult
AUTHOR
Paul Curtz, Aug 28 2009
EXTENSIONS
Offset set to 1 by R. J. Mathar, Sep 06 2009
STATUS
approved

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Last modified June 14 04:12 EDT 2024. Contains 373393 sequences. (Running on oeis4.)