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A141673
Triangle T(n,m) read by rows: T(n,1) = n; T(n,m) = A008683(n)*n/m if m is a divisor of n, where m = 2..n, otherwise T(n,m) = 0.
1
1, 2, -1, 3, 0, -1, 4, 0, 0, 0, 5, 0, 0, 0, -1, 6, 3, 2, 0, 0, 1, 7, 0, 0, 0, 0, 0, -1, 8, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 10, 5, 0, 0, 2, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1
OFFSET
1,2
COMMENTS
The function here is Mats Granvik's idea: my effort is coding it and entering it in the OEIS. All of it is based on Gary W. Adamson's A126988.
EXAMPLE
Triangle begins
{ 1},
{ 2, -1},
{ 3, 0, -1},
{ 4, 0, 0, 0},
{ 5, 0, 0, 0, -1},
{ 6, 3, 2, 0, 0, 1},
{ 7, 0, 0, 0, 0, 0, -1},
{ 8, 0, 0, 0, 0, 0, 0, 0},
{ 9, 0, 0, 0, 0, 0, 0, 0, 0},
{10, 5, 0, 0, 2, 0, 0, 0, 0, 1}
MATHEMATICA
t[n_, m_] = If[m == 1, n, If[Mod[n, m] == 0, MoebiusMu[n]*n/m, 0]]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
PROG
(PARI) T(n, m) = if (m==1, n, if (n % m, 0, moebius(n)*n/m));
tabl(nn) = for (n=1, nn, for (m=1, n, print1(T(n, m), ", ")); print); \\ Michel Marcus, Jun 10 2018
CROSSREFS
KEYWORD
sign,tabl,easy
AUTHOR
STATUS
approved