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A366444
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Triangle read by rows: T(n,k) = phi(n/k)*A023900(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
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1
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1, 1, -1, 2, 0, -2, 2, -1, 0, -1, 4, 0, 0, 0, -4, 2, -2, -2, 0, 0, 2, 6, 0, 0, 0, 0, 0, -6, 4, -2, 0, -1, 0, 0, 0, -1, 6, 0, -4, 0, 0, 0, 0, 0, -2, 4, -4, 0, 0, -4, 0, 0, 0, 0, 4, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 4, -2, -4, -2, 0, 2, 0, 0, 0, 0, 0, 2
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = phi(n/k)*A023900(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
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EXAMPLE
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{
{1}, = 1
{1, -1}, = 0
{2, 0, -2}, = 0
{2, -1, 0, -1}, = 0
{4, 0, 0, 0, -4}, = 0
{2, -2, -2, 0, 0, 2}, = 0
{6, 0, 0, 0, 0, 0, -6}, = 0
{4, -2, 0, -1, 0, 0, 0, -1}, = 0
{6, 0, -4, 0, 0, 0, 0, 0, -2}, = 0
{4, -4, 0, 0, -4, 0, 0, 0, 0, 4}, = 0
{10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}, = 0
{4, -2, -4, -2, 0, 2, 0, 0, 0, 0, 0, 2} = 0
}
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MATHEMATICA
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nn = 12; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Flatten[Table[Table[If[Mod[n, k] == 0, EulerPhi[n/k]*g[k], 0], {k, 1, n}], {n, 1, nn}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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