A063676 a(1) = 1 and for n > 1 let a(n) = a(n-1) + m, where m is the arithmetic mean of the largest subset of all predecessors such that m is an integer and m is maximal.

1, 2, 4, 7, 11, 16, 24, 33, 46, 62, 78, 106, 140, 184, 235, 302, 391, 487, 612, 768, 943, 1155, 1367, 1698, 2075, 2513, 3023, 3649, 4386, 5286, 6306, 7544, 8936, 10408, 12255, 14102, 16590, 19426, 22902, 26902, 31345, 36634, 42707, 49486, 57463