OFFSET
1,3
COMMENTS
Records: a(3^(n-1)) = n and a(k) < n for k < 3^(n-1).
Multiplicative because A051064 is. - Andrew Howroyd, Jul 28 2018
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Indranil Ghosh)
FORMULA
a(n) = A051064(n) if n is odd, 0 otherwise.
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/2. - Amiram Eldar, Sep 11 2020
From Amiram Eldar, Dec 27 2022: (Start)
Multiplicative with a(2^e) = 0, a(3^e) = e+1, and a(p^e) = 1 if p >= 5.
Dirichlet g.f.: zeta(s)*(1-1/2^s)/(1-1/3^s). (End)
EXAMPLE
a(27) = 4 because 2^27 + 1 = 134217729 = 3^4 * 19 * 87211.
MATHEMATICA
Table[If[OddQ[n], IntegerExponent[3n, 3], 0], {n, 100}] (* Indranil Ghosh, Mar 27 2017 *)
PROG
(Magma) [IsEven(n) select 0 else Factorization(3*n)[1][2]: n in [1..87]];
(PARI) a(n) = if(n%2, if(n<1, 0, 1 + valuation(n, 3)), 0); \\ Indranil Ghosh, Mar 27 2017
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
Jon E. Schoenfield, Mar 26 2017
STATUS
approved