%I #25 Feb 28 2023 06:48:11

%S 4,6,8,10,16,20,28,32,64,70,88,104,110,120,128,136,152,256,464,496,

%T 512,592,650,672,884,1024,1155,1888,1952,2048,2144,4030,4096,5830,

%U 8128,8192,8384,8925,11096,16384,17816,18632,18904,30240,32128,32445,32760,32768

%N Near-multiperfects with primes excluded, abs(sigma(m) mod m) <= log(m).

%C Sequences A117346 through A117350 are an attempt to improve on sequences A045768 through A045770, A077374, A087167, A087485 and A088007 through A088012 and related sequences (but not to replace them) by using a more significant definition of "near". E.g., is sigma(n) (where sigma is the sum-of-divisors function) really "near" a multiple of n, for n = 9? Or n = 18?

%D R. K. Guy, Unsolved Problems in Number Theory, B2.

%H Amiram Eldar, <a href="/A117347/b117347.txt">Table of n, a(n) for n = 1..10000</a>

%H Walter Nissen, <a href="http://upforthecount.com/math/nearmpf.html">Near Multiperfects</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect Number</a>

%F sigma(m) = k * m + r, abs(r) <= log(m).

%e 70 is a term because sigma(70) = 144 = 2 * 70 + 4, while 4 < log(70) ~= 4.248.

%Y Cf. A045768, A045769, A045770, A077374, A087167, A087485.

%Y Cf. A088007, A088008, A088009, A088010, A088011, A088012.

%Y Cf. A117346, A117348, A117349, A117350.

%K nonn

%O 1,1

%A _Walter Nissen_, Mar 09 2006

%E Offset corrected by _Amiram Eldar_, Mar 05 2020