OFFSET
1
COMMENTS
Same negative sum as in the recurrence for the Möbius function except that it is applied at all the divisors and not only in the first column. The table therefore acts as a prime number sieve giving the characteristic sequence of prime numbers in the first column. Row sums are 1,0,0,0,0,0,0,0,0,...
FORMULA
T(n, k) = If n = k then 1 else if k divides n then -Sum_{i=k+1..n} T(n, i) else T(n,k) = 0.
EXAMPLE
{
{1},
{-1, 1},
{-1, 0, 1},
{0, -1, 0, 1},
{-1, 0, 0, 0, 1},
{0, 0, -1, 0, 0, 1},
{-1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, -1, 0, 0, 0, 1},
{0, 0, -1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, -1, 0, 0, 0, 0, 1},
{-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1}
}
MATHEMATICA
(* recurrence *) Clear[t, n, k, nn]; nn = 12; t[n_, k_] := t[n, k] = If[n == k, 1, If[Mod[n, k] == 0, -Sum[t[n, i], {i, k + 1, n}], 0]]; Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, nn}]]
CROSSREFS
KEYWORD
sign
AUTHOR
Mats Granvik, Mar 29 2016
STATUS
approved