A074625 Triangular array T(n,k) (n >= 1, 1 <= k <= n) read by rows, where T(n,k) = smallest number x such that Mod[sigma[x],n]=k.

1, 1, 3, 1, 7, 2, 1, 5, 2, 3, 1, 4, 2, 3, 8, 1, 7, 2, 3, 2401, 5, 1, 29, 2, 3, 6, 5, 4, 1, 10, 2, 3, 9, 5, 4, 7, 1, 19, 2, 3, 13, 5, 4, 7, 10, 1, 6, 2, 3, 8, 5, 4, 7, 18, 19, 1, 9, 2, 3, 24, 5, 4, 7, 16, 21, 43, 1, 13, 2, 3, 2401, 5, 4, 7, 49, 31213, 9604, 6, 1, 8, 2, 3, 10, 5, 4, 7, 33, 22

Offset: 1

Author

Labos Elemer, Aug 26 2002

Keywords

• nonn
• tabl

Comments

In the table output, one can observe constant diagonals (or lines in the square output). The indices of these are: 1, 3, 4, 6, 7, 8, 12, 13, ... (see A002191). And the corresponding values are: 1, 2, 3, 5, 4, 7, 6, 9, ... (see A002192). - Michel Marcus, Dec 19 2013

Examples

			Triangle begins
1;
1,3;
1,7,2;
1,5,2,3;
1,4,2,3,8; ...
		

Crossrefs

Cf. A000203, A028982, A074384, A074386, A072461, A072462, A072862.

Programs

Mathematica

{k=0, s=0, fl=1}; Table[Print["#"]; Table[fl=1; Print[{r, m}]; Do[s=Mod[DivisorSigma[1, n], m]; If[(s==r)&&(fl==1), Print[n]; fl=0], {n, 1, 150000}], {r, 0, m-1}], {m, 1, 25}]

Formula

Min{x; Mod[sigma[x], n]=r}, r=1..n, n=1, ...