A178062 Triangle t(n,m) = -A000396(n)+A000396(m)+A000396(n-m) read by rows.

1, 1, 1, 1, -16, 1, 1, -462, -462, 1, 1, -7626, -8072, -7626, 1, 1, -33542202, -33549812, -33549812, -33542202, 1, 1, -8556318714, -8589860900, -8589868064, -8589860900, -8556318714, 1, 1, -128848822266, -137405140964, -137438682704

Offset: 0

Author

Roger L. Bagula, May 18 2010

Keywords

• sign
• tabl

Comments

The definition is based on the definition of a perfect number A000396(0) = 1.

Row sums are 1, 2, -14, -922, -23322, -134184026, ... = 2*(A092336(n)+1) -(n+1)*A000396(n). - R. J. Mathar, Nov 26 2010

Examples

			1;
1, 1;
1, -16, 1;
1, -462, -462, 1;
1, -7626, -8072, -7626, 1;
1, -33542202, -33549812, -33549812, -33542202, 1;
1, -8556318714, -8589860900, -8589868064, -8589860900, -8556318714, 1;
1, -128848822266, -137405140964, -137438682704, -137438682704, -137405140964, -128848822266, 1;
1, -2305842870701260794, -2305842999550083044, -2305843008106401296, -2305843008139935872, -2305843008106401296, -2305842999550083044, -2305842870701260794, 1;
		

Crossrefs

Cf. A000396.

Programs

Mathematica

a={1,6,28,496,8128,33550336, 8589869056,137438691328,2305843008139952128,
2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216}
t[n_,m_]:=(-a[[n+1]]+(a[[m+1]]+a[[n-m+1]]));
Table[Table[t[n,m],{m,0,n}],{n,0,10}];
Flatten[%]

Formula

t(n,m) = t(n,n-m).