A139421 a(1)=1; for n>1, a(n) = largest prime divisor of n!!.

1, 2, 3, 2, 5, 3, 7, 3, 7, 5, 11, 5, 13, 7, 13, 7, 17, 7, 19, 7, 19, 11, 23, 11, 23, 13, 23, 13, 29, 13, 31, 13, 31, 17, 31, 17, 37, 19, 37, 19, 41, 19, 43, 19, 43, 23, 47, 23, 47, 23, 47, 23, 53, 23, 53, 23, 53, 29, 59, 29, 61, 31, 61, 31, 61, 31, 67, 31, 67, 31, 71, 31, 73, 37