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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

LINKS

Table of n, a(n) for n=2..87.

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]]

CROSSREFS

Cf. A001055, A045778, A050376, A220418, A220420, A273866, A273873, A289501, A290261, A290262, A290971, A290973, A295279, A295632, A295635.

Sequence in context: A335434 A264440 A303386 * A050334 A295279 A316784

Adjacent sequences:  A295633 A295634 A295635 * A295637 A295638 A295639

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 24 2017

STATUS

approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)