bibkey: firoozbakht2004a092028 authors: Farideh Firoozbakht year: 2004 title: “OEIS A092028, a(n) is the smallest m > 1 such that m divides n^m-1” doi: null url: https://oeis.org/A092028 claim: “A092028 %N: a(n) is the smallest m > 1 such that m divides n^m-1. A092028 %C: Each prime factor of n-1 is a solution of the equation n^x-1 == 0 (mod x), so a(n) is not greater than the 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). A092028 %A: Farideh Firoozbakht, Mar 26 2004. A092028 %O: 3,1” strata_touched:

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OEIS A092028

The entry defines a(n) as the smallest m > 1 such that m divides n^m-1. The formal definition uses the natural infimum and therefore assigns zero when the defining set is empty.

The entry records two conjectures. The formal theorem proves Conjecture 2 for every n > 2; Conjecture 1 then follows from primality of the least prime factor of n-1.

Verified locator

• URL: https://oeis.org/A092028
• Locator: COMMENTS, “Conjecture 1: All terms of this sequence are primes.”
• Locator: COMMENTS, “Conjecture 2: a(n) is the smallest prime factor of n-1 or for n>2, A092028(n) = A020639(n-1).”