A037458 a(1)=1; for n > 1, a(n)=n-a(n-sqrtint(n)) where sqrtint(n) denotes floor(sqrt(n)).

1, 1, 2, 3, 3, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 38