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Sum over all subsets of {1,..,n} of the GCD of the subset.
3

%I #11 Aug 30 2019 04:19:50

%S 1,4,10,22,42,84,154,298,568,1108,2142,4254,8362,16636,33076,66004,

%T 131556,262974,525136,1050016,2098756,4196962,8391288,16782312,

%U 33559612,67118176,134227594,268453714,536889198,1073777718,2147519572

%N Sum over all subsets of {1,..,n} of the GCD of the subset.

%H Amiram Eldar, <a href="/A065568/b065568.txt">Table of n, a(n) for n = 1..3321</a>

%t Sum[Plus @@ GCD @@@ KSubsets[Range[n], m], {m, n}] (* or *)

%t Table[Sum[Plus@@(EulerPhi[Divisors[k]] 2^(k/Divisors[k]))/2, {k, n}], {n, 42}]

%Y Row sums of A065567, first differences equal A034738,

%K nonn

%O 1,2

%A _Wouter Meeussen_, Nov 30 2001