a(n) = number of m such that sum of proper divisors of m (A001065(m)) is 2*n.
0, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 1, 2, 0, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 2, 1, 2, 4, 2, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 1, 3, 2, 1, 3, 1, 1, 0, 2, 2, 2, 3, 2, 1, 1, 0, 1, 2, 1, 2, 1, 1
1
By separating A048138(n) into even and odd n, we obtain better information about how this sequence behaves. The odd part is shown in S000867. Note that this even part grows very slowly. See where records occur in S000871.
T. D. Noe, Plot of 10000 terms
T. D. Noe, Table of 10000 terms
Wikipedia, Divisor function
(Mma) nn = 200; s = Table[0, {nn}]; Do[k = DivisorSigma[1, n] - n; If[0 < k <= nn, s[[k]]++], {n, nn^2}]; Take[s, {2, nn, 2}]
Cf. A001065, A048138, S000867, S000871.
nonn
T. D. Noe, May 03 2016