Superperfect number
Generalizations
Perfect and superperfect numbers are examples of the wider class of m-superperfect numbers, which satisfy corresponding to m=1 and 2 respectively.

Superperfect number

Section Title: Generalizations
Table Section Text: Perfect and superperfect numbers are examples of the wider class of m-superperfect numbers, which satisfy corresponding to m=1 and 2 respectively.

m	k	(m,k)-perfect numbers	OEIS sequence

2	2	2, 4, 16, 64, 4096, 65536, 262144	A019279

2	3	8, 21, 512	A019281

2	4	15, 1023, 29127	A019282

2	6	42, 84, 160, 336, 1344, 86016, 550095, 1376256, 5505024	A019283

2	7	24, 1536, 47360, 343976	A019284

2	8	60, 240, 960, 4092, 16368, 58254, 61440, 65472, 116508, 466032, 710400, 983040, 1864128, 3932160, 4190208, 67043328, 119304192, 268173312, 1908867072	A019285

2	9	168, 10752, 331520, 691200, 1556480, 1612800, 106151936	A019286

2	10	480, 504, 13824, 32256, 32736, 1980342, 1396617984, 3258775296	A019287

2	11	4404480, 57669920, 238608384	A019288

2	12	2200380, 8801520, 14913024, 35206080, 140896000, 459818240, 775898880, 2253189120	A019289

3	any	12, 14, 24, 52, 98, 156, 294, 684, 910, 1368, 1440, 4480, 4788, 5460, 5840, ...	A019292

4	any	2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 26, 32, 39, 42, 60, 65, 72, 84, 96, 160, 182, ...	A019293

Sentence(s)

The perfect numbers are: 2, 4, 16, 64, 4096, 65536, 262144 (sequence A019279 in the OEIS).

final_sentence: The perfect numbers are: 2, 4, 16, 64, 4096, 65536, 262144 (sequence A019279 in the OEIS).