Can you find a formula or rule for the nth term of a sequence related to the prime numbers or prime factorizations so that the initial terms of the sequence have these values?
a) 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, . . .
b) 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, . . .
c) 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, . . .
d) 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, . . .
e) 1, 2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, . . .
f) 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, . . .