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

1,14

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.

Links

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

Example

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

Mathematica

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}]

Prog

(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

Crossrefs

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

Sequence in context: A196056 A161095 A276162 * A236548 A249949 A155798

Adjacent sequences: A118104 A118105 A118106 * A118108 A118109 A118110

Keyword

nonn

Author

T. D. Noe, Apr 13 2006

Status

approved