(define $φ (lambda [$n] (* n (product (map (lambda [$p] (- 1 (/ 1 p))) (unique (p-f n))))))) (take 100 (map2 2#[%1 %2 (p-f %2)] nats (map φ nats))) {[1 1 {}] [2 1 {}] [3 2 {2}] [4 2 {2}] [5 4 {2 2}] [6 2 {2}] [7 6 {2 3}] [8 4 {2 2}] [9 6 {2 3}] [10 4 {2 2}] [11 10 {2 5}] [12 4 {2 2}] [13 12 {2 2 3}] [14 6 {2 3}] [15 8 {2 2 2}] [16 8 {2 2 2}] [17 16 {2 2 2 2}] [18 6 {2 3}] [19 18 {2 3 3}] [20 8 {2 2 2}] [21 12 {2 2 3}] [22 10 {2 5}] [23 22 {2 11}] [24 8 {2 2 2}] [25 20 {2 2 5}] [26 12 {2 2 3}] [27 18 {2 3 3}] [28 12 {2 2 3}] [29 28 {2 2 7}] [30 8 {2 2 2}] [31 30 {2 3 5}] [32 16 {2 2 2 2}] [33 20 {2 2 5}] [34 16 {2 2 2 2}] [35 24 {2 2 2 3}] [36 12 {2 2 3}] [37 36 {2 2 3 3}] [38 18 {2 3 3}] [39 24 {2 2 2 3}] [40 16 {2 2 2 2}] [41 40 {2 2 2 5}] [42 12 {2 2 3}] [43 42 {2 3 7}] [44 20 {2 2 5}] [45 24 {2 2 2 3}] [46 22 {2 11}] [47 46 {2 23}] [48 16 {2 2 2 2}] [49 42 {2 3 7}] [50 20 {2 2 5}] [51 32 {2 2 2 2 2}] [52 24 {2 2 2 3}] [53 52 {2 2 13}] [54 18 {2 3 3}] [55 40 {2 2 2 5}] [56 24 {2 2 2 3}] [57 36 {2 2 3 3}] [58 28 {2 2 7}] [59 58 {2 29}] [60 16 {2 2 2 2}] [61 60 {2 2 3 5}] [62 30 {2 3 5}] [63 36 {2 2 3 3}] [64 32 {2 2 2 2 2}] [65 48 {2 2 2 2 3}] [66 20 {2 2 5}] [67 66 {2 3 11}] [68 32 {2 2 2 2 2}] [69 44 {2 2 11}] [70 24 {2 2 2 3}] [71 70 {2 5 7}] [72 24 {2 2 2 3}] [73 72 {2 2 2 3 3}] [74 36 {2 2 3 3}] [75 40 {2 2 2 5}] [76 36 {2 2 3 3}] [77 60 {2 2 3 5}] [78 24 {2 2 2 3}] [79 78 {2 3 13}] [80 32 {2 2 2 2 2}] [81 54 {2 3 3 3}] [82 40 {2 2 2 5}] [83 82 {2 41}] [84 24 {2 2 2 3}] [85 64 {2 2 2 2 2 2}] [86 42 {2 3 7}] [87 56 {2 2 2 7}] [88 40 {2 2 2 5}] [89 88 {2 2 2 11}] [90 24 {2 2 2 3}] [91 72 {2 2 2 3 3}] [92 44 {2 2 11}] [93 60 {2 2 3 5}] [94 46 {2 23}] [95 72 {2 2 2 3 3}] [96 32 {2 2 2 2 2}] [97 96 {2 2 2 2 2 3}] [98 42 {2 3 7}] [99 60 {2 2 3 5}] [100 40 {2 2 2 5}]}