cp's OEIS Frontend

A118107 Period of the vector sequence d(n)^2^k mod n for k=1,2,3,..., where d(n) is the vector of divisors of n.

%I A118107 #7 Sep 23 2018 20:57:58
%S A118107 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,2,4,1,1,1,2,1,2,1,1,1,1,4,1,
%T A118107 2,2,1,6,2,1,1,2,1,4,2,10,1,1,1,4,1,2,1,6,4,2,6,3,1,1,1,4,2,1,1,4,1,1,
%U A118107 10,2,1,2,1,6,4,6,4,2,1,1,1,4,1,2,1,3,3,4,1,2,2,10,4,11,6,1,1,6,4,4
%N A118107 Period of the vector sequence d(n)^2^k mod n for k=1,2,3,..., where d(n) is the vector of divisors of n.
%C A118107 This sequence is related to the period of sigma_(2^k)(n) mod n, which is important in studying the numbers n dividing sigma_(2^k)(n) for all k>0. See A066292 and A118076. Note that a(n)=1 if n is a power of a prime.
%H A118107 Antti Karttunen, <a href="/A118107/b118107.txt">Table of n, a(n) for n = 1..65537</a>
%e A118107 See A118106 for an example involving d(n)^k.
%t A118107 Table[d=Divisors[n]; k=0; found=False; While[i=0; While[i<k-1 && !found, i++; found=(dk[i]==dk[k])]; !found, k++; dk[k]=PowerMod[d,2^k,n]]; k-i, {n,100}]
%o A118107 (PARI) A118107(n) = { my(divs=apply(d -> (d%n),divisors(n)), odivs = Vec(divs), vs = Map()); mapput(vs, odivs, 0); for(k=1,oo,divs = vector(#divs,i,(divs[i]*divs[i])%n); if(mapisdefined(vs, divs), return(k-mapget(vs, divs)), mapput(vs, divs, k))); }; \\ _Antti Karttunen_, Sep 23 2018
%Y A118107 Cf. A118106 (period of the vector sequence d(n)^k mod n).
%K A118107 nonn
%O A118107 1,14
%A A118107 _T. D. Noe_, Apr 13 2006