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

0,5

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

Links

Table of n, a(n) for n=0..31.

Formula

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

Example

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;

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[%]

Crossrefs

Cf. A000396.

Sequence in context: A022179 A015141 A176390 * A040263 A082696 A040262

Adjacent sequences: A178059 A178060 A178061 * A178063 A178064 A178065

Keyword

sign,tabl

Author

Roger L. Bagula, May 18 2010

Status

approved