OFFSET
3,1
LINKS
Robert Israel, Table of n, a(n) for n = 3..1665
Shinsaku Fujita, alpha-beta Itemized Enumeration of Inositol Derivatives and m-Gonal Homologs by Extending Fujita's Proligand Method, Bull. Chem. Soc. Jpn. 2017, 90, 343-366; doi:10.1246/bcsj.20160369. See Table 8.
FORMULA
From Robert Israel, Aug 23 2018 after Fujita (2017), Eq. (100)(set n=2, m=n): (Start)
if n is even, a(n) = (4*n)^(-1)*(Sum_{d|n, d odd} phi(d)*4^(n/d) - 2^(n-1).
if n is odd, a(n) = (4*n)^(-1)*Sum_{d|n} phi(d)*4^(n/d) - 2^(n-1). (End)
MAPLE
f:= proc(n) uses numtheory;
if n::even then (4*n)^(-1)*add(phi(d)*4^(n/d), d = select(type, divisors(n), odd)) - 2^(n-1)
else (4*n)^(-1)*add(phi(d)*4^(n/d), d = divisors(n)) - 2^(n-1)
fi
end proc:
map(f, [$3..50]); # Robert Israel, Aug 23 2018
MATHEMATICA
a[n_] := If[EvenQ[n], (4n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Select[ Divisors[n], OddQ]}] - 2^(n-1), (4n)^(-1) Sum[EulerPhi[d] 4^(n/d), {d, Divisors[n]}] - 2^(n-1)];
Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Mar 23 2019, after Robert Israel *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 01 2017
STATUS
approved