
COMMENTS

By convention, for n = 1, a(1) = 1 with q = 1.
The corresponding pairs (tau(n), q) are (1, 1), (4, 2), (8, 3), (6, 2), (16, 2), (10, 2), (24, 2), (36, 6), (48, 3), (48, 3), (14, 2), (48, 6), (72, 3), (96, 2), (96, 2), (72, 7), (72, 7), (72, 5), (80, 2), (120, 8), (120, 6), (216, 2), (384, 3), (432, 3), (240, 3), (320, 2), (360, 5), (26, 2), (384, 5), (384, 2), (288, 9).
Properties of this sequence:
q = 2 if n = 1, 6, 28, 120, 496, 672, 8128, ... is a multiplyperfect number (see A007691 where it is conjectured that this sequence is infinite), which would imply that this sequence is also infinite because A007691 is a subsequence.


EXAMPLE

24 is in the sequence because the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, and the sum 1/24 + 1/12 + 1/8 + 1/6 + 1/4 + 1/3 = 1.
28 is in the sequence because 28 is a multiplyperfect number: the divisors are 1, 2, 4, 7, 14, 28, and the sum of the reciprocals of all the divisors is 1/28 + 1/14 + 1/7 + 1/4 + 1/2 + 1 = 2.
