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A118107
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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.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,14
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COMMENTS
| This sequence is related to the period of sigma_(2^k)(n) mod n, which is important in verifying the 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.
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EXAMPLE
| See A118106 for an example involving d(n)^k.
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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}]
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CROSSREFS
| Cf. A118106 (period of the vector sequence d(n)^k mod n).
Sequence in context: A107435 A196056 A161095 * A155798 A055652 A154844
Adjacent sequences: A118104 A118105 A118106 * A118108 A118109 A118110
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Apr 13 2006
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