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

Author

Leroy Quet, Oct 30 2007

Keywords

• nonn
• tabf

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.

Examples

			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
		

Crossrefs

Cf. A038566, A000010.

Programs

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 *)

Extensions

Extended by Ray Chandler, Nov 01 2007