A382752 Numbers k such that A000005(k) = A065295(k).

6, 7, 8, 9, 10, 13, 19, 23, 29, 32, 37, 47, 54, 71, 109, 149, 167, 173, 223, 229, 263, 283, 359, 383, 479, 503, 509, 653, 659, 719, 739, 773, 839, 863, 887, 971, 983, 1229, 1319, 1367, 1439, 1487, 1493, 1637, 1699, 1823, 1949, 1997, 2039, 2063, 2207, 2309, 2411, 2447

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 02 2025

Keywords

• nonn

Examples

			6 is a term because the number of divisors of 6 is equal to 4 (1, 2, 3 and 6) and 1^1 = 1 (mod 6), 2^2 = 4 (mod 6), 3^3 = 27 == 3 (mod 6), 4^4 = 256 == 4 (mod 6), 5^5 + 3125 == 5 (mod 6).
		

Crossrefs

Cf. A000005, A065295.

Programs

Magma

[k: k in [2..2500] | #Divisors(k) eq #[s: s in [0..k-1] | s^s mod k eq s]];

PARI

isok(k) = numdiv(k) == sum(s=1, k-1, Mod(s, k)^s == s); \\ Michel Marcus, Jun 03 2025