%I #16 Apr 19 2024 03:30:25
%S 0,1,1,2,3,4,5,8,7,10,10,14,14,16,16,22,20,26,24,30,28,34,30,43,36,43,
%T 40,51,44,56,49,63,55,66,55,78,64,75,70,89,72,93,77,98,87,103,84,122,
%U 94,115,104,127,102,136,109,141,123,143,117,170,128,153,138,174,138,183,143,183,161,189,152,224,163,200,180
%N a(n) = Sum_{k = 1..ceiling(n/2)} [u_2(k)*u_2(n+1-k)], where u_2(k) is number of unordered factorization k = i*j (A038548).
%C An analog of A055507 for unordered factorizations.
%C For background references see A330570.
%H Amiram Eldar, <a href="/A330573/b330573.txt">Table of n, a(n) for n = 0..10000</a>
%t s[n_] := s[n] = Ceiling[DivisorSigma[0, n]/2]; a[n_] := Sum[s[k]*s[n + 1 - k], {k, 1, Ceiling[n/2]}]; Array[a, 100, 0] (* _Amiram Eldar_, Apr 19 2024*)
%Y Cf. A000005, A038548, A055507.
%Y See A330572 for another version.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jan 08 2020
%E Offset and name corrected by _Amiram Eldar_, Apr 19 2024