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A092028
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a(n) is the smallest number m such that m is greater than 1 and m divides n^m-1.
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4
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2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 73, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| Each prime factor of n-1 is a solution of the equation Mod[n^x-1,x]=0, so a(n) is not greater than smallest prime factor of n-1. Conjecture 1: All terms of this sequence are primes. Conjecture 2: a(n) is the smallest prime factor of n-1 or For n>2 A092028(n)=A020639(n-1).
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FORMULA
| a[n_] := (For[k=2, Mod[n^k-1, k]>0, k++ ];k)
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EXAMPLE
| a(8)=7 because 7 divides 8^7-1 and there doesn't exist an m such that 1<m<7 and m divides 8^m-1.
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MATHEMATICA
| a[n_] := (For[k=2, Mod[n^k-1, k]>0, k++ ]; k); Table[a[n], {n, 3, 75}]
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CROSSREFS
| Cf. A020639.
Sequence in context: A085308 A086286 A135679 * A020639 A092067 A079879
Adjacent sequences: A092025 A092026 A092027 * A092029 A092030 A092031
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KEYWORD
| nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 26 2004
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