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a(n) = A063776(2*n) + 1.
1

%I #26 Aug 18 2018 08:35:32

%S 3,5,13,33,105,345,1173,4097,14573,52433,190653,699073,2581113,

%T 9586985,35791473,134217729,505290273,1908874585,7233629133,

%U 27487790721,104715393913,399822410105,1529755308213,5864062017537,22517998136937,86607685141745

%N a(n) = A063776(2*n) + 1.

%H Vincenzo Librandi, <a href="/A283844/b283844.txt">Table of n, a(n) for n = 1..1000</a>

%H Juhani Karhumäki, S. Puzynina, M. Rao, M. A. Whiteland, <a href="https://arxiv.org/abs/1605.03319">On cardinalities of k-abelian equivalence classes</a>, arXiv preprint arXiv:1605.03319 [math.CO], 2016.

%F See Karhumäki et al. (2016), Proposition 7.4.

%t Table[a=Select[Divisors[n], OddQ[#]&]; (1 + Apply[Plus, 2^(n/a)EulerPhi[a]]/n), {n, 2, 52, 2}] (* _Vincenzo Librandi_, Mar 29 2017 *)

%o (PARI) a(n) = my(m = 2*n); 1 + sumdiv(m, d, (d%2)* 2^(m/d)*eulerphi(d))/m; \\ _Michel Marcus_, Aug 18 2018

%Y Cf. A063776.

%Y A bisection of A283843.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Mar 28 2017