Knödel numbers - Find Kn The Knödel numbers are a set of sequences. Specifically, the Knödel numbers for a positive integer \$n\$ are the set of composite numbers \$m\$, such that all \$i &lt; m\$, coprime to \$m\$, satisfy \$i^{(m-n)} \equiv 1 \mod m\$. The set of Knödel numbers for a specific \$n\$ is denoted \$K_n\$. (Wikipedia).
For example, \$K_1\$ are the Carmichael numbers, and OEIS A002997. They go like: \$\{561, 1105, 1729, 2465, 2821, 6601, ... \}\$. \$K_2\$ is OEIS A050990 and goes like, \$\{4, 6, 8, 10, 12, 14, 22, 24, 26, ... \}\$.
Your task
Your task is to write a program/function/etc. that takes two numbers, \$n\$ and \$p\$. It should return the first \$p\$ numbers of the Knödel Sequence, \$K_n\$.
This is code-golf, so shortest code in bytes wins!
Examples
1, 6   -&gt;   [561, 1105, 1729, 2465, 2821, 6601]
2, 3   -&gt;   [4, 6, 8]
4, 9   -&gt;   [6, 8, 12, 16, 20, 24, 28, 40, 44]
3, 1   -&gt;   [9]
3, 0   -&gt;   []
21, 21 -&gt;   [45, 57, 63, 85, 105, 117, 147, 231, 273, 357, 399, 441, 483, 585, 609, 651, 741, 777, 861, 903, 987]
Pyth, 29 28 bytes

.f&amp;tPZ!f&amp;q1iTZt%^T-ZQZSZvzhQ


1 byte saved thanks to Jakube and orlp.

Demonstration.

Input in the form

p
n


A fairly straightforward calculation. Relative primeness is checked via Pyth's gcd function. This code showcases .f, Pyth's "first n satisfying" function.

I have incorporated the implicit condition that m &gt; n by starting the search for m values at n + 1.