A132066 Irregular array: the sum of the first m terms of row n is the m-th positive divisor of n.

1, 1, 1, 1, 2, 1, 1, 2, 1, 4, 1, 1, 1, 3, 1, 6, 1, 1, 2, 4, 1, 2, 6, 1, 1, 3, 5, 1, 10, 1, 1, 1, 1, 2, 6, 1, 12, 1, 1, 5, 7, 1, 2, 2, 10, 1, 1, 2, 4, 8, 1, 16, 1, 1, 1, 3, 3, 9, 1, 18, 1, 1, 2, 1, 5, 10, 1, 2, 4, 14, 1, 1, 9, 11, 1, 22, 1, 1, 1, 1, 2, 2, 4, 12, 1, 4, 20, 1, 1, 11, 13, 1, 2, 6, 18, 1, 1, 2, 3

Offset

1,5

Comments

Row n contains A000005(n) terms.

Links

Table of n, a(n) for n=1..99.

Example

The positive divisors of 20 are 1,2,4,5,10,20. Row 20 of the array is 1,1,2,1,5,10. So we have 1=1; 1+1=2; 1+1+2=4; 1+1+2+1=5; 1+1+2+1+5=10; 1+1+2+1+5+10=20.
The first 10 rows:
1;
1,1;
1,2;
1,1,2;
1,4;
1,1,1,3
1,6;
1,1,2,4;
1,2,6;
1,1,3,5

Mathematica

f[n_] := Block[{d}, d = Divisors[n]; d - Prepend[Most[d], 0]]; Flatten[Array[f, 40]] (* Ray Chandler, Nov 01 2007 *)

Crossrefs

Cf. A027750, A000005.

Sequence in context: A046067 A342416 A305531 * A102190 A138650 A266685

Adjacent sequences: A132063 A132064 A132065 * A132067 A132068 A132069

Keyword

nonn,tabf

Author

Leroy Quet, Oct 30 2007

Extensions

Extended by Ray Chandler, Nov 01 2007

Status

approved