A375488 Numbers k such that k^(sigma(k) - k) == k (mod sigma(k)), where sigma = A000203.

1, 2, 3, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 23, 27, 29, 31, 32, 33, 35, 36, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 79, 83, 87, 89, 91, 95, 97, 98, 99, 101, 103, 107, 109, 112, 113, 119, 127, 131, 135, 136, 137, 139, 143, 145, 149, 151, 157, 161, 163, 167, 173, 179, 181, 191, 193, 195, 197, 199

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 17 2024

Keywords

• nonn

Examples

			9 is in this sequence because 9^(sigma(9) - 9) = 9^(13 - 9) = 9^4 = 6561 modulo 13 is equal to 9.
		

Crossrefs

Supersequence of A000040.

Cf. A000203, A001065.

Programs

Magma

[1] cat [k: k in [2..200] | k^(SumOfDivisors(k)-k) mod SumOfDivisors(k) eq k];

PARI

isok(k) = Mod(k, sigma(k))^(sigma(k) - k) == k; \\ Michel Marcus, Aug 18 2024