A074634 Cototient-remainder triangle: triangular array T(n,k) (n >= 1, 0 <= k < n) read by rows, where T(n,k) = smallest number x such that cototient(x) mod n = k.

1, 1, 2, 1, 2, 4, 1, 2, 4, 9, 1, 2, 4, 9, 6, 1, 2, 4, 9, 6, 25, 1, 2, 4, 9, 6, 18, 10, 1, 2, 4, 9, 6, 25, 10, 15, 1, 2, 4, 9, 6, 25, 10, 15, 12, 1, 2, 4, 9, 6, 25, 10, 15, 12, 21, 1, 2, 4, 9, 6, 24, 10, 15, 12, 21, 45, 1, 2, 4, 9, 6, 25, 10, 15, 12, 21, 30, 35, 1, 2, 4, 9, 6, 25, 10, 15, 12

Offset

1,3

Links

Table of n, a(n) for n=1..87.

Formula

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

Example

1; 1,2; 1,2,4; 1,2,4,9; 1,2,4,9,6; 1,2,4,9,6,25; 1,2,4,9,6,18,10; 1,2,4,9,6,25,10,15; 1,2,4,9,6,25,10,15,12, ...

Mathematica

{k=0, s=0, fl=1}; Table[Print["#"]; Table[fl=1; Print[{r, m}]; Do[s=Mod[n-EulerPhi[n], m]; If[(s==r)&&(fl==1), Print[n]; fl=0], {n, 1, 500}], {r, 0, m-1}], {m, 1, 50}]

Crossrefs

Cf. A051953, A074625.

Sequence in context: A256009 A123937 A138882 * A152036 A035015 A212829

Adjacent sequences: A074631 A074632 A074633 * A074635 A074636 A074637

Keyword

nonn,tabl

Author

Labos Elemer, Aug 29 2002

Extensions

Name modified to match data by Sean A. Irvine, Jan 22 2025

Status

approved