Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Dec 03 2015 04:31:04
%S 1,10,39,148,405,1254,3143,8488,20853,52050,123915,297804,692237,
%T 1611974,3687795,8405584,18939921,42512562,94634003,209819940,
%U 462431697,1015269486,2218786839,4832458392,10485762025,22684180610,48922424415,105229923596
%N a(n) = n * Sum_{d|n} d*2^(d-1).
%H Colin Barker, <a href="/A074225/b074225.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane and Thomas Wieder, <a href="http://arXiv.org/abs/math.CO/0307064">The Number of Hierarchical Orderings</a>, arXiv:math/0307064 [math.CO], 2003.
%H N. J. A. Sloane and Thomas Wieder, <a href="http://dx.doi.org/10.1007/s11083-004-9460-9">The Number of Hierarchical Orderings</a>, Order 21 (2004), 83-89.
%t a[n_] := n*DivisorSum[n, #*2^(#-1)&]; Array[a, 30] (* _Jean-François Alcover_, Dec 03 2015 *)
%o (PARI) vector(100, n, n*sumdiv(n, d, d*2^(d-1))) \\ _Colin Barker_, Jan 29 2015
%Y Equals n*A083413(n).
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jun 15 2003