A055006 a(n) is the least multiple of n such that a(n) = 1 mod k for all integers k with 1 < k < n and k relatively prime to n.

1, 2, 3, 4, 25, 6, 301, 736, 2241, 190, 25201, 4236, 83161, 19306, 64065, 135136, 7207201, 85086, 49008961, 49468420, 36951201, 27776386, 698377681, 855189336, 25700298625, 2445441076, 74364290001, 13624600276, 2248776129601, 6254036790, 39594522567601

Offset: 1

Author

Stephen G Penrice, May 30 2000

Keywords

• nonn

Programs

Mathematica

Table[Block[{m = 1, t = Select[Range[2, n - 1], CoprimeQ[#, n] &]}, While[! AllTrue[t, Mod[m n, #] == 1 &], m++]; m n], {n, 20}] (* Michael De Vlieger, Mar 08 2022 *)

PARI

isok(m, n) = for (k=2, n-1, if ((gcd(k, n)==1) && ((m % k) !=1), return(0))); return(1);
a(n) = my(m=n); while (!isok(m,n), m+=n); m; \\ Michel Marcus, Mar 08 2022

Extensions

More terms from Sean A. Irvine, Mar 07 2022