Arjun Maneesh Agarwal - cp's OEIS frontend

User: Arjun Maneesh Agarwal

Arjun Maneesh Agarwal has authored 1 sequences.

A386207 Numbers m > 1 such that there exists k such that k | m, k^k = k mod m and 1 < k < m.

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 98, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116

Offset: 1

Arjun Maneesh Agarwal, Jul 15 2025

nonn

The sequence seems to be very similar to A324455 but there are terms present here, which are absent there and vice versa. Also, the k satisfying the property for a given n, even when it exists, is different for both.
The sequence is infinite as A016825 (4m+2, m > 0) is a subsequence with the corresponding k = 2m + 1.
Another subsequence is A002997 (Carmichael numbers).

			6 is a term as 3^3 = 27 = 3 mod 6.
10 is a term as 5^5 = 3125 = 5 mod 10.

Arjun Maneesh Agarwal, Table of n, a(n) for n = 1..10000

Cf. A324455, A016825, A002997.

divisors n = [x | x <- [2..n], n `mod` x == 0]
property n = any (\x -> x^x `mod` n == x) $ divisors n
inRange t = [x | x <- [2..t], property x]

isok(m) = fordiv(m, k, if((k>1) && (kMichel Marcus, Jul 16 2025

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User: Arjun Maneesh Agarwal

A386207 Numbers m > 1 such that there exists k such that k | m, k^k = k mod m and 1 < k < m.

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