A113793 Triangle read by rows: T(n,m) = phi(n - m + 1) * phi(m), n >= 1, m >= 1.

1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 4, 4, 4, 2, 6, 2, 8, 4, 8, 2, 6, 4, 6, 4, 8, 8, 4, 6, 4, 6, 4, 12, 4, 16, 4, 12, 4, 6, 4, 6, 8, 12, 8, 8, 12, 8, 6, 4, 10, 4, 12, 8, 24, 4, 24, 8, 12, 4, 10, 4, 10, 8, 12, 16, 12, 12, 16, 12, 8, 10, 4, 12, 4, 20, 8, 24, 8, 36, 8, 24, 8, 20, 4, 12

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Aug 25 2008

Keywords

• nonn
• tabl

Examples

			{1},
{1, 1},
{2, 1, 2},
{2, 2, 2, 2},
{4, 2, 4, 2, 4},
{2, 4, 4, 4, 4, 2},
{6, 2, 8, 4, 8, 2, 6},
{4, 6, 4, 8, 8, 4, 6, 4},
{6, 4, 12, 4, 16, 4, 12, 4, 6},
{4, 6, 8, 12, 8, 8, 12, 8, 6, 4},
{10, 4, 12, 8, 24, 4, 24, 8, 12, 4, 10}
		

Crossrefs

Column 1 and leading diagonal give A000010.

Middle diagonal gives A127473.

Row sums give A065093.

Programs

Mathematica

T[n_, m_] = EulerPhi[n - m + 1]*EulerPhi[m + 1]; Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Formula

T(n,m) = A000010(m)*A000010(n-m+1), n >= 1, m >= 1. - Omar E. Pol, Jan 14 2025

Extensions

Name corrected and more terms added by Omar E. Pol, Jan 14 2025