A153216 A triangular sequence of powers ( suppressed powers) : t(n,m)=m^Sum[Floor[n/m^k], {k, 1, Infinity}].

2, 2, 3, 8, 3, 4, 8, 3, 4, 5, 16, 9, 4, 5, 6, 16, 9, 4, 5, 6, 7, 128, 9, 16, 5, 6, 7, 8, 128, 81, 16, 5, 6, 7, 8, 9, 256, 81, 16, 25, 6, 7, 8, 9, 10, 256, 81, 16, 25, 6, 7, 8, 9, 10, 11, 1024, 243, 64, 25, 36, 7, 8, 9, 10, 11, 12

Offset: 2

Author

Roger L. Bagula, Dec 20 2008

Keywords

• nonn
• tabl

Comments

Row sums are:

{2, 5, 15, 20, 40, 47, 179, 260, 418, 429, 1449,...}. I use:

t(n,m)=m^Sum[Floor[n/m^k], {k, 1, 12}];

for the sake of time ( answer is the same at lower powers).

Examples

			{2},
{2, 3},
{8, 3, 4},
{8, 3, 4, 5},
{16, 9, 4, 5, 6},
{16, 9, 4, 5, 6, 7},
{128, 9, 16, 5, 6, 7, 8},
{128, 81, 16, 5, 6, 7, 8, 9},
{256, 81, 16, 25, 6, 7, 8, 9, 10},
{256, 81, 16, 25, 6, 7, 8, 9, 10, 11},
{1024, 243, 64, 25, 36, 7, 8, 9, 10, 11, 12}
		

Programs

Mathematica

Table[Table[m^Sum[Floor[n/m^k], {k, 1, 12}], {m, 2, n}], {n, 2, 12}]
Flatten[%]

Formula

t(n,m)=m^Sum[Floor[n/m^k], {k, 1, Infinity}].