A185358 - OEIS

%I #30 May 08 2021 08:35:58

%S 1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,5,1,1,

%T 1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,5,1,1,1,1,

%U 1,1,1,3,1,1,1,1,1,1,1,3,4,1,1,1

%N The period of the sequence i^i (mod n) starts from i=a(n).

%H G. C. Greubel, <a href="/A185358/b185358.txt">Table of n, a(n) for n = 1..5000</a>

%H R. Hampel, <a href="https://doi.org/10.4064/ap-1-2-360-366">The length of the shortest period of rests of numbers n^n</a>, Ann. Polon. Math. 1 (1955), 360-366.

%F If n = Product_{pi^ei} then a(n) = Max_{1- pi*(1+floor[-ei/pi])}.

%t a[p_,e_]:=1- p*(1+Floor[-e/p]);a[n_]:=Max@Module[{fa=FactorInteger[n]},Table[a[fa[[i,1]],fa[[i,2]]],{i,1,Length[fa]}]];Table[a[n],{n,1,84}]

%o (Python)

%o from sympy import factorint, floor

%o def a(n):

%o     f=factorint(n)

%o     return 1 if n==1 else max(1 - i*(1 + (-f[i])//i) for i in f)

%o print([a(n) for n in range(1, 201)]) # _Indranil Ghosh_, Jun 29 2017

%Y Cf. A185359.

%K nonn

%O 1,8

%A _José María Grau Ribas_, Jan 21 2012