OFFSET
1,2
COMMENTS
Sequence differs from A143512 beginning with a(970).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = 2.
Let m_a(n) = (-1)^A010060(n), if n is squarefree, and 0, otherwise (a-analog of Möbius function). Then Sum_{n>=1} m_a(n)/a(n) = 1/2.
A generalization: Sum_{n>=1} 1/(a(n))^s = Product_{Fermat numbers F} (1-F^(-s))^(-1), where s>0 (an analog of Euler identity for primes, where, for real s, s>1).
EXAMPLE
9 = 3^2 is a term since 3 is in A001317.
MATHEMATICA
f[n_] := FromDigits[Table[Mod[Binomial[n, k], 2], {k, 0, n}], 2]; n = 13; v = Array[f, n, 0]; vmax = v[[-1]]; s = {1}; Do[v1 = v[[k]]; rmax = Floor[Log[v1, vmax]]; s1 = v1^Range[0, rmax]; s2 = Select[Union[Flatten[Outer[Times, s, s1]]], # <= vmax &]; s = Union[s, s2], {k, 2, n}]; s (* Amiram Eldar, Sep 27 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 01 2010
EXTENSIONS
Offset corrected and more terms added by Amiram Eldar, Sep 27 2020
STATUS
approved