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%I #12 Jul 19 2015 01:01:17
%S 2,2,2,4,6,10,18,32,56,102,186,340,630,1170,2182,4096,7710,14560,
%T 27594,52428,99858,190650,364722,699040,1342176,2581110,4971008,
%U 9586980,18512790,35791358,69273666,134217728,260300986,505290270,981706806
%N Number of subsets of {1,2,..n} that sum to 1 mod n.
%H <a href="/index/Su#subsetsums">Index entries for sequences related to subset sums modulo m</a>
%F a(n) = 1/n * sum_{d divides n and d is odd} 2^(n/d) * mu(d); (mu(d) is the Moebius function, sequence A008683).
%e a(7)=18 because there are 18 subsets of {1,2,3,4,5,6,7} which sum to 1 mod 7:{1}, {1,7}, {2,6}, {3,5}, {1,2,5}, {1,3,4}, {2,6,7}, {3,5,7}, {4,5,6}, {1,2,5,7}, {1,3,4,7}, {1,3,5,6}, {2,3,4,6}, {4,5,6,7}, {1,2,3,4,5}, {1,3,5,6,7}, {2,3,4,6,7}, {1,2,3,4,5,7}.
%t f[n_] := Block[{d = Select[Divisors@n, OddQ@ # &]}, Plus @@ (2^(n/d)*MoebiusMu@d)/n]; Array[f, 35] (* _Robert G. Wilson v_, Feb 20 2006 *)
%Y Cf. A063776, A008683. Equals 2*A000048(n).
%K nonn
%O 1,1
%A Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 25 2001
%E More terms from _Vladeta Jovovic_, Sep 27 2001
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