1,1

{T(n,k)*k, k=1..n} setminus {0} = divisors of n; sum(T(n,k)*(k^i),k=1..n) = sigma[i](n) = sum of the i-th power of positive divisors of n; sum(T(n,k),k=1..n)=A000005, sum(T(n,k)*k,k=1..n)=A000203

Row sums are A000005. Diagonal sums are A032741(n+2). Might be called a Mobius matrix. Binomial transform (product by binomial matrix) is A101508. - Paul Barry (pbarry(AT)wit.ie), Dec 05 2004

A054525 = the inverse of this triangle = A129360 * A115369. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 15 2007

Mats Granvik, Illustration of A051731

T(n, k)=T(n-k, k) for k<=n/2, T(n, k)=0 for n/2<k<=n-1, T(n, n)=1

Rows given by A074854 converted to binary. Example: A074854(4)= 13(decimal)= 1101(binary); row 4 = 1, 1, 0, 1. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Oct 04 2003

Columns have g.f. x^k/(1-x^(k+1)) (k>=0). - Paul Barry (pbarry(AT)wit.ie), Dec 05 2004

Matrix inverse of triangle A054525, where A054525(n, k) = MoebiusMu(n/k) if k|n, 0 otherwise. - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 09 2006

Equals = A129372 * A115361 as infinite lower triangular matrices. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 15 2007

This triangle * [1,2,3,...] = Sigma(n), A000203: (1, 3, 4, 7, 6, 12, 8,...). A051731 * [1/1, 1/2, 1/3,...] = Sigma(n)/n: (1/1, 3/2, 4/3, 7/4, 6/5,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2007

{1}; {1,1}; {1,0,1}; {1,1,0,1}; {1,0,0,0,1}; ...

Cf. A000005, A000203, A074854, A054525, A129372, A115361.

Sequence in context: A054524 A110471 A103994 this_sequence A135839 A120529 A099443

Adjacent sequences: A051728 A051729 A051730 this_sequence A051732 A051733 A051734

easy,nice,nonn,tabl

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)