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A320167 Regular triangle where T(n,k) = Sum (-1)^i, where the sum is over all factorizations of n into i factors that are all > 1 and <= k. 0
1, 0, -1, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

LINKS

Table of n, a(n) for n=1..84.

FORMULA

T(1,k) = 1, T(n,k) = -Sum_{d|n, 1 < d <= k} T(n/d,d).

EXAMPLE

Triangle begins:

  1

  0 -1

  0  0 -1

  0  1  1  0

  0  0  0  0 -1

  0  0  1  1  1  0

  0  0  0  0  0  0 -1

  0 -1 -1  0  0  0  0 -1

  0  0  1  1  1  1  1  1  0

  0  0  0  0  1  1  1  1  1  0

  0  0  0  0  0  0  0  0  0  0 -1

  0  0 -1  0  0  1  1  1  1  1  1  0

  0  0  0  0  0  0  0  0  0  0  0  0 -1

  0  0  0  0  0  0  1  1  1  1  1  1  1  0

  0  0  0  0  1  1  1  1  1  1  1  1  1  1  0

  0  1  1  1  1  1  1  2  2  2  2  2  2  2  2  1

  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1

  0  0 -1 -1 -1  0  0  0  1  1  1  1  1  1  1  1  1  0

  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1

  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  1  0

MATHEMATICA

u[n_, k_]:=If[n==1, 1, -Sum[u[n/d, d], {d, Select[Rest[Divisors[n]], #<=k&]}]]

Table[u[n, k], {n, 20}, {k, n}]

CROSSREFS

Cf. A001055, A045778, A066032, A114592, A162247, A316441, A319237, A319238, A320835, A320836.

Cf. A195017, A281118, A317145, A317176, A330935.

Sequence in context: A129569 A266611 A286752 * A030658 A187950 A112539

Adjacent sequences:  A320164 A320165 A320166 * A320168 A320169 A320170

KEYWORD

sign,tabl

AUTHOR

Gus Wiseman, Oct 22 2018

STATUS

approved

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)