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A295636
Write 2 - Zeta(s) in the form Product_{n > 1}(1 - a(n)/n^s).
2
1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 8, 1, 2, 2, 4, 1, 6, 1, 6, 2, 2, 2, 8, 1, 2, 2, 8, 1, 6, 1, 4, 4, 2, 1, 16, 1, 4, 2, 4, 1, 8, 2, 8, 2, 2, 1, 16, 1, 2, 4, 8, 2, 6, 1, 4, 2, 6, 1, 24, 1, 2, 4, 4, 2, 6, 1, 16, 3, 2, 1, 16, 2, 2, 2
OFFSET
2,5
FORMULA
a(n) = Sum_t (-1)^(v(t)-1) where the sum is over all strict tree-factorizations of n (see A295279 for definition) and v(t) is the number of nodes (branchings and leaves) in t.
MATHEMATICA
nn=100;
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
-Solve[Table[-1==Sum[Times@@a/@f, {f, Select[facs[n], UnsameQ@@#&]}], {n, 2, nn}], Table[a[n], {n, 2, nn}]][[1, All, 2]]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 24 2017
STATUS
approved