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%I #24 Mar 31 2022 03:14:21
%S 12,36,104,352,1172,4119,14572,52492,190652,699266,2581112,9587602,
%T 35791472,134219859,505290272,1908881998,7233629132,27487817244,
%U 104715393912,399822505942,1529755308212,5864062368274,22517998136936
%N a(n) = (1/(2n)) * Sum_{d|n} phi(d) * 2^(2n/d) + (2^((n-4)/2), if n is even).
%C Previous name was "Number of orientations of an n-cycle". Apparently, the book by Harary and Palmer erroneously gives this formula for the number of orientations of an n-cycle, but the correct sequence for that is A053656. The error is in the exponent of 2 in the sum; it should be n/d, not 2*n/d. - _Pontus von Brömssen_, Mar 30 2022
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 129, (5.3.3).
%H Amiram Eldar, <a href="/A058880/b058880.txt">Table of n, a(n) for n = 3..1666</a>
%F a(n) = (1/(2n)) * Sum_{d|n} phi(d) * 2^(2n/d) + (2^((n-4)/2), if n is even). - _Amiram Eldar_, Aug 28 2019
%p A058880 := proc(n) local d,t1,t2; if n mod 2 = 0 then t1 := 2^((n-4)/2) else t1 := 0; fi; t2 := divisors(n); for d in t2 do t1 := t1+phi(d)*2^(2*n/d)/(2*n); od; t1; end;
%t a[n_] := DivisorSum[n, EulerPhi[#]*2^(2n/#) &]/(2n) + If[OddQ[n], 0, 2^((n - 4)/2)]; Array[a, 23, 3] (* _Amiram Eldar_, Aug 28 2019 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d)*2^(2*n/d))/(2*n) + if (!(n%2), 2^((n-4)/2)); \\ _Michel Marcus_, Aug 29 2019
%Y Cf. A053656.
%K nonn
%O 3,1
%A _N. J. A. Sloane_, Jan 07 2001
%E New name, using existing formula, from _Pontus von Brömssen_, Mar 30 2022
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