A375790 Numbers k such that (sigma(k) - k)^(sigma(k) - k) == k (mod sigma(k)), where sigma = A000203.

1, 9, 10, 112, 136, 514, 528, 625, 652, 1072, 1152, 1216, 1984, 2016, 2956, 3808, 4320, 4672, 5056, 6592, 8716, 9801, 10432, 13552, 29632, 32896, 38476, 40096, 47296, 72256, 117649, 148960, 174592, 181000, 232128, 245025, 246208, 288832, 289216, 355492, 392448, 405952, 419392, 458752, 499968

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 29 2024

Keywords

• nonn

Examples

			9 is in this sequence because (sigma(9)-9)^(sigma(9)-9) = (13-4)^(13-4) = 256 modulo 13 equal to 9.
		

Crossrefs

Cf. A000203, A001065, A036878, A375488.

Programs

Magma

[k: k in [1..50000] | (SumOfDivisorse(k)-k)^(SumOfDivisorse(k)-k) mod SumOfDivisors(k) eq k];

PARI

isok(k) = my(s=sigma(k)); Mod(s-k, s)^(s-k) == k \\ Michel Marcus, Aug 29 2024

Extensions

More terms from Michel Marcus, Aug 29 2024