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

1,4

Links

Table of n, a(n) for n=1..91.

Formula

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

Example

{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}

Mathematica

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

Crossrefs

Column 1 and leading diagonal give A000010.

Middle diagonal gives A127473.

Row sums give A065093.

Sequence in context: A025859 A031281 A203181 * A289499 A215904 A083552

Adjacent sequences: A113790 A113791 A113792 * A113794 A113795 A113796

Keyword

nonn,tabl,changed

Author

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

Extensions

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

Status

approved