A114896 A symmetrical triangle of weight coefficients using the Divisors Sigma function: t(n,m) = Sigma_0(n-m+1)*Sigma_0(m+1).

1, 2, 2, 2, 4, 2, 3, 4, 4, 3, 2, 6, 4, 6, 2, 4, 4, 6, 6, 4, 4, 2, 8, 4, 9, 4, 8, 2, 4, 4, 8, 6, 6, 8, 4, 4, 3, 8, 4, 12, 4, 12, 4, 8, 3, 4, 6, 8, 6, 8, 8, 6, 8, 6, 4, 2, 8, 6, 12, 4, 16, 4, 12, 6, 8, 2

Offset

0,2

Comments

Row sums are {1, 4, 8, 14, 20, 28, 37, 44, 58, 64, 80}.

Links

G. C. Greubel, Rows n=0..100 of triangle, flattened

Formula

t(n,m) = Sigma_0(n - m + 1)*Sigma_0(m + 1), where Sigma_0(n) = A000005(n).

Example

Triangle begins
  {1},
  {2,  2},
  {2,  4,  2},
  {3,  4,  4,  3},
  {2,  6,  4,  6,  2},
  {4,  4,  6,  6,  4,  4},
  {2,  8,  4,  9,  4,  8,  2},
  {4,  4,  8,  6,  6,  8,  4,  4},
  {3,  8,  4, 12,  4, 12,  4,  8,  3},
  {4,  6,  8,  6,  8,  8,  6,  8,  6,  4},
  {2,  8,  6, 12,  4, 16,  4, 12,  6,  8,  2}

Mathematica

t[n_, m_] =DivisorSigma[0, n - m + 1]*DivisorSigma[0, m + 1]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]//Flatten

Prog

(PARI) for(n=0, 20, for(m=0, n, print1(numdiv(n-m+1)*numdiv(m+1), ", "))) \\ G. C. Greubel, Jun 08 2018
(Magma) [[NumberOfDivisors(n-m+1)*NumberOfDivisors(m+1): m in [0..n]]: n in [0..20]]; // G. C. Greubel, Jun 08 2018

Crossrefs

Cf. A000005.

Sequence in context: A368468 A069930 A086327 * A216620 A181019 A066761

Adjacent sequences: A114893 A114894 A114895 * A114897 A114898 A114899

Keyword

nonn,tabl

Author

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

Status

approved