A074792 Least k > 1 such that k^n == 1 (mod n).

2, 3, 4, 3, 6, 5, 8, 3, 4, 9, 12, 5, 14, 13, 16, 3, 18, 5, 20, 3, 4, 21, 24, 5, 6, 25, 4, 13, 30, 11, 32, 3, 34, 33, 36, 5, 38, 37, 16, 3, 42, 5, 44, 21, 16, 45, 48, 5, 8, 9, 52, 5, 54, 5, 16, 13, 7, 57, 60, 7, 62, 61, 4, 3, 66, 23, 68, 13, 70, 29, 72, 5, 74, 73, 16, 37, 78, 17, 80, 3

Offset

1,1

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

If p is prime a(p)=p+1 and a(2p)=2p-1; if n is in A050384 a(n)=n+1; if n is in A067945 a(n)=3 etc. It seems that sum(k=1, n, a(k)) is asymptotic to c*n^2 with c=0.2...

Mathematica

Do[k = 2; While[ !IntegerQ[(k^n - 1)/n], k++ ]; Print[k], {n, 1, 80}] (* Robert G. Wilson v *)

Prog

(PARI) a(n)=if(n<0, 0, s=2; while((s^n-1)%n>0, s++); s)
(PARI) a(n)=my(s=2); while(Mod(s, n)^n-1!=0, s++); return(s) \\ Rémy Sigrist, Apr 02 2017

Crossrefs

a(n) = {A076944(n)}^(1/n).

Cf. A076942, A076943, A076944.

Sequence in context: A126214 A126801 A076945 * A321168 A341313 A341312

Adjacent sequences: A074789 A074790 A074791 * A074793 A074794 A074795

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Status

approved