A161856 Triangle read by rows in which row n lists the coefficients of the interpolating polynomial for its divisors of n.

1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 0, 2, 1, 6, 1, 1, 1, 1, 1, 2, 4, 1, 1, 2, 0, 1, 10, 1, 1, 0, 0, 1, 1, 1, 12, 1, 1, 4, -2, 1, 2, 0, 8, 1, 1, 1, 1, 1, 1, 16, 1, 1, 0, 2, -4, 12, 1, 18, 1, 1, 1, -2, 7, -11, 1, 2, 2, 8, 1, 1, 8, -6, 1, 22, 1, 1, 0, 0, 1, -3, 8, -12, 1, 4, 16, 1, 1, 10, -8, 1, 2, 4, 8, 1, 1

Offset

1,5

Comments

EDP(n,x) = SUM(a(A006218(n)-1+i)*A007318(x,i-1): 1<=i<=A000005(n)) is the interpolating polynomial for the divisors of n, see also A161700;

A000005(n) = length of n-th row, i.e. same length as n-th row in A027750;

sum of n-th row, n>1: A161857(n) = SUM(a(A006218(n-1)+i): 1<=i<=A000005(n));

a(A006218(n)+1) = 1.

Links

R. Zumkeller, Table of rows 1..1000, flattened

R. Zumkeller, Enumerations of Divisors

Example

1; 1,1; 1,2; 1,1,1; 1,4; 1,1,0,2; 1,6; 1,1,1,1; 1,2,4; ... .

Crossrefs

A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A080856, A161711, A161712, A161713, A006261, A161715.

Sequence in context: A362490 A118210 A061399 * A122944 A107688 A060097

Adjacent sequences: A161853 A161854 A161855 * A161857 A161858 A161859

Keyword

sign,tabf

Author

Reinhard Zumkeller, Jun 20 2009

Status

approved