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EXAMPLE
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factim(5,1) = -90+190*i. Hence a(5) = 190.
Asymptotic linearity for the type 2 prime p = 5: the sequence of 5-adic valuations [ v_5(a(n)) : n = 1..100] = [0, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 6, 5, 6, 6, 7, 6, 6, 7, 7, 7, 8, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 11, 11, 11, 13, 11, 12, 12, 13, 12, 12, 13, 13, 13, 14, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 18, 19, 18, 18, 18, 19, 19, 19, 20, 19, 20, 21, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 24, 25, 24, 24, 24, 25, 25, 25].
Note that v_5(a(100)) = 25 = 100/(5 - 1), in line with Moll's conjecture 5.5 above.
Oscillatory behavior for the type 3 prime p = 3: the sequence of 3-adic valuations [ v_3(a(n)) : n = 1..100] = [0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0]. It appears that v_3(a(n)) = 0 unless n == 0 or 2 (mod 6). (End)
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