假设f(n)=σ(n)-n,即n的真因子和，如果n是完全数，那么f(n)=n.
以某个正整数n开始，如果f(n)=n或者f(n)=1,就停止，否则继续迭代下去。
那么，是否对任意n，迭代的结果都是1或者一个完全数？
第一个迭代比较长的数是138：
138, 150, 222, 234, 312, 528, 960, 2088,3762, 5598, 6570, 10746,13254, 13830, 19434, 20886, 21606, 25098, 26742, 26754,40446, 63234, 77406, 110754, 171486, 253458, 295740, 647748, 1077612, 1467588, 1956812,2109796, 1889486, 953914, 668966, 353578, 176792, 254128, 308832, 502104,753216, 1240176, 2422288, 2697920, 3727264, 3655076, 2760844, 2100740, 2310856,2455544, 3212776, 3751064, 3282196, 2723020, 3035684, 2299240, 2988440,5297320, 8325080, 11222920, 15359480, 19199440, 28875608, 25266172, 19406148,26552604, 40541052, 54202884, 72270540, 147793668, 228408732, 348957876,508132204, 404465636, 303708376, 290504024, 312058216, 294959384, 290622016, 286081174,151737434, 75868720, 108199856, 101437396, 76247552, 76099654, 42387146,21679318, 12752594, 7278382, 3660794, 1855066, 927536, 932464, 1013592,1546008, 2425752, 5084088, 8436192, 13709064, 20563656, 33082104, 57142536,99483384, 245978376, 487384824, 745600776, 1118401224, 1677601896, 2538372504,4119772776, 8030724504, 14097017496, 21148436904, 40381357656, 60572036544, 100039354704,179931895322, 94685963278, 51399021218, 28358080762, 18046051430, 17396081338,8698040672, 8426226964, 6319670230, 5422685354, 3217383766, 1739126474,996366646, 636221402, 318217798, 195756362, 101900794, 54202694, 49799866,24930374, 17971642, 11130830, 8904682, 4913018, 3126502, 1574810, 1473382,736694, 541162, 312470, 249994, 127286, 69898, 34952, 34708, 26038, 13994, 7000,11720, 14740, 19532, 16588, 18692, 14026, 7016, 6154, 3674, 2374, 1190, 1402,704, 820, 944, 916, 694, 350, 394, 200, 265, 59, 1
下一个是276，目前还没算出结果。