This sequence should include odd perfect numbers too, if they exist.
There are no other terms below 2*10^9.
abundancy(k) k 2k sigma(k) abundance
1.99480519480519 1155 2310 2304 -6
2.00067226890756 8925 17850 17856 6
2.00018492834027 32445 64890 64896 6
2.00001356346004 442365 884730 884736 6
2.00000011318610 159030135 318060270 318060288 18
1.99999999264376 815634435 1631268870 1631268864 -6
2.00000000695943 2586415095 5172830190 5172830208 18
As it happens, abundance of these is -6, 6 or 18. This is not necessarily true for larger terms. (End)
a(8) <= 221753180448460815.
a(9) <= 3278298202600507814120339275775985.
221753180448460815 and 3278298202600507814120339275775985 are also terms of this sequence and their abundances are -30 and 30 respectively. In fact, 3278298202600507814120339275775985 and 815634435 are the only odd terms known where abs(sigma(k)-2k) <= log_10(k). (End)
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