A332002 Number of compositions (ordered partitions) of n into distinct parts all relatively prime to n.
1, 1, 0, 2, 2, 4, 2, 12, 4, 6, 4, 64, 4, 132, 6, 32, 32, 616, 6, 1176, 32, 120, 58, 4756, 32, 3452, 108, 1632, 132, 30460, 8, 55740, 376, 3872, 352, 18864, 132, 315972, 1266, 13368, 352, 958264, 108, 1621272, 2228, 10176, 6166, 4957876, 352, 2902866, 2132
Offset: 0
Keywords
Examples
a(9) = 6 because we have [8, 1], [7, 2], [5, 4], [4, 5], [2, 7] and [1, 8].
Links
Programs
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Maple
a:= proc(n) local b; b:= proc(m, i, p) option remember; `if`(m=0, p!, `if`(i<1, 0, b(m, i-1, p)+`if`(i>m or igcd(i, n)>1, 0, b(m-i, i-1, p+1)))) end; forget(b): b(n$2, 0) end: seq(a(n), n=0..63); # Alois P. Heinz, Feb 04 2020 -
Mathematica
a[n_] := Module[{b}, b[m_, i_, p_] := b[m, i, p] = If[m == 0, p!, If[i < 1, 0, b[m, i-1, p] + If[i > m || GCD[i, n] > 1, 0, b[m-i, i-1, p+1]]]]; b[n, n, 0]]; a /@ Range[0, 63] (* Jean-François Alcover, Nov 26 2020, after Alois P. Heinz *)