A373047 Least k with exactly n partitions k = x + y + z satisfying sigma*(k) = sigma*(x) + sigma*(y) + sigma*(z), where sigma*(k) is the sum of the anti-divisors of k.
11, 33, 16, 20, 26, 37, 40, 19, 43, 46, 93, 91, 80, 76, 39, 78, 155, 103, 74, 135, 128, 152, 116, 117, 190, 104, 187, 138, 168, 147, 160, 223, 208, 403, 281, 173, 163, 170, 250, 243, 272, 257, 258, 232, 222, 278, 266, 245, 352, 253, 279, 256, 288, 295, 231, 291
Offset: 1
Examples
a(7) = 40 and 40 has 7 partitions of three numbers, x, y and z, for which sigma*(65) = sigma*(x) + sigma*(y) + sigma*(z) = 55. In fact: sigma*(1) + sigma*+(4) + sigma*(35) = 0 + 3 + 52 = 55; sigma*(1) + sigma*(12) + sigma*(27) = 0 + 13 + 42 = 55; sigma*(1) + sigma*(14) + sigma*(25) = 0 + 16 + 39 = 55; sigma*(4) + sigma*(14) + sigma*(22) = 3 + 16 + 36 = 55; sigma*(5) + sigma*(8) + sigma*(27) = 5 + 8 + 42 = 55; sigma*(9) + sigma*(13) + sigma*(18) = 8 + 19 + 28 = 55; sigma*(10) + sigma*(12) + sigma*(18) = 14 + 13 + 28 = 55; Furthermore 40 is the minimum number to have this property.