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.

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, 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, 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

Offset: 1

Author

T. D. Noe, Apr 13 2006

Keywords

• nonn

Comments

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.

Examples

			See A118106 for an example involving d(n)^k.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A118106 (period of the vector sequence d(n)^k mod n).

Programs

Mathematica

Table[d=Divisors[n]; k=0; found=False; While[i=0; While[i
				

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