A132068 Irregular array: row n has A000010(n) terms: the sum of the first m terms of row n is the m-th positive integer which is coprime to n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 2, 2, 1, 1, 2, 3, 1, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 4, 2, 4, 1, 1, 1

Offset

1,6

Comments

The first term of each row is 1. The sum of the terms of row n is n-1, for n>=2. After the initial 1, the remaining terms of each row are the same forward or backward.

Links

Table of n, a(n) for n=1..105.

Example

The positive integers which are <= 12 and are coprime to 12 are 1,5,7,11. Row 12 of the array is: 1,4,2,4. So we have: 1=1; 1+4=5; 1+4+2=7; 1+4+2+4=11.
The first 12 rows of the array:
1;
1;
1,1;
1,2;
1,1,1,1;
1,4;
1,1,1,1,1,1;
1,2,2,2;
1,1,2,1,2,1;
1,2,4,2;
1,1,1,1,1,1,1,1,1,1;
1,4,2,4

Mathematica

f[n_] := Block[{g}, g = Select[Range[n], GCD[ #, n] == 1 &]; g - Prepend[Most[g], 0]]; Flatten[Array[f, 25]] (* Ray Chandler, Nov 01 2007 *)

Crossrefs

Cf. A038566, A000010.

Sequence in context: A247487 A010248 A325403 * A173441 A326851 A129192

Adjacent sequences: A132065 A132066 A132067 * A132069 A132070 A132071

Keyword

nonn,tabf

Author

Leroy Quet, Oct 30 2007

Extensions

Extended by Ray Chandler, Nov 01 2007

Status

approved