Jelly, 9 bytes
1Æs4¡÷\Ƒ#
A full program accepting k m n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
1Æs4¡÷\Ƒ# - Main Link: k, m
1 # - count up from j=1 & find the first (3rd argument, n) truthy results of f(j, k):
Ƒ - is (j) invariant under?:
\ - last two links as a dyad - g(j, k):
¡ - repeated application...
4 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by k)
Jelly, 9 bytes
1Æs4¡÷\Ƒ#
A full program accepting k m n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
1Æs4¡÷\Ƒ# - Main Link: k, m
1 # - count up from j=1 & find the first (3rd argument, n) truthy results of f(j, k):
Ƒ - is (j) invariant under?:
\ - last two links as a dyad - g(j, k):
¡ - repeated application...
4 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by k)
Jelly, 9 bytes
1Æs4¡÷\Ƒ#
A full program accepting k m n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
1Æs4¡÷\Ƒ# - Main Link: k
1 # - count up from j=1 & find the first (3rd argument, n) truthy results of f(j, k):
Ƒ - is (j) invariant under?:
\ - last two links as a dyad - g(j, k):
¡ - repeated application...
4 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by k)
Jelly, 9 bytes
Æs3¡÷$=ð#1Æs4¡÷\Ƒ#
A full program accepting m k m n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
The smallest \$k\$-\$m\$-generalised-perfect-number must be greater than or equal to \$m\$ since the sum of the divisors of any number greater than one is at least one greater than itself (since it is a divisor of itself).
Æs3¡÷$=ð#1Æs4¡÷\Ƒ# - Main Link: mk, km
1 ð## - count up from j=mj=1 & find the first (3rd argument, n) truthy results of f(j, k):
$ Ƒ - is (j) invariant under?:
\ - last two links as a monaddyad - g(j, k):
¡ ¡ - repeated application...
3 4 - ...number of times: 1st argument, m
Æs Æs - ...action: divisor sum
÷ ÷ - divide (by j)
= - equals (k)?
Jelly, 9 bytes
Æs3¡÷$=ð#
A full program accepting m k n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
The smallest \$k\$-\$m\$-generalised-perfect-number must be greater than or equal to \$m\$ since the sum of the divisors of any number greater than one is at least one greater than itself (since it is a divisor of itself).
Æs3¡÷$=ð# - Main Link: m, k
ð# - count up from j=m & find the first (3rd argument, n) truthy results of f(j, k):
$ - last two links as a monad - g(j):
¡ - repeated application...
3 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by j)
= - equals (k)?
Jelly, 9 bytes
1Æs4¡÷\Ƒ#
A full program accepting k m n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
1Æs4¡÷\Ƒ# - Main Link: k, m
1 # - count up from j=1 & find the first (3rd argument, n) truthy results of f(j, k):
Ƒ - is (j) invariant under?:
\ - last two links as a dyad - g(j, k):
¡ - repeated application...
4 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by k)
Jelly, 9 bytes
Æs3¡÷$=ð#
A full program accepting m k n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
The smallest \$k\$-\$m\$-generalised-perfect-number must be greater than or equal to \$k\$\$m\$ since the sum of the divisors of any number greater than one is at least one greater than itself (since it is a divisor of itself).
Æs3¡÷$=ð# - Main Link: m, k
ð# - count up from j=m & find the first (3rd argument, n) truthy results of f(j, k):
$ - last two links as a monad - g(j):
¡ - repeated application...
3 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by j)
= - equals (k)?
Jelly, 9 bytes
Æs3¡÷$=ð#
A full program accepting m k n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
The smallest \$k\$-\$m\$-generalised-perfect-number must be greater than or equal to \$k\$ since the sum of the divisors of any number greater than one is at least one greater than itself (since it is a divisor of itself).
Æs3¡÷$=ð# - Main Link: m, k
ð# - count up from j=m & find the first (3rd argument, n) truthy results of f(j, k):
$ - last two links as a monad - g(j):
¡ - repeated application...
3 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by j)
= - equals (k)?
Jelly, 9 bytes
Æs3¡÷$=ð#
A full program accepting m k n which prints a list representation of the first n \$k\$-\$m\$-generalised-perfect-numbers.
How?
The smallest \$k\$-\$m\$-generalised-perfect-number must be greater than or equal to \$m\$ since the sum of the divisors of any number greater than one is at least one greater than itself (since it is a divisor of itself).
Æs3¡÷$=ð# - Main Link: m, k
ð# - count up from j=m & find the first (3rd argument, n) truthy results of f(j, k):
$ - last two links as a monad - g(j):
¡ - repeated application...
3 - ...number of times: 1st argument, m
Æs - ...action: divisor sum
÷ - divide (by j)
= - equals (k)?