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%I #21 Feb 28 2023 06:48:06
%S 6,10,20,28,70,88,104,110,120,136,152,464,496,592,650,672,884,1155,
%T 1888,1952,2144,4030,5830,8128,8384,8925,11096,17816,18632,18904,
%U 30240,32128,32445,32760,32896,33664,45356,70564,77744,85936,91388,100804,116624
%N Near-multiperfects with primes, powers of 2 and 6 * prime excluded, abs(sigma(n) mod n) <= log(n).
%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) really "near" a multiple of n, for n=9? Or n=18? Log is the natural logarithm. Sigma is the sum_of_divisors function.
%D R. K. Guy, Unsolved Problems in Number Theory, B2.
%H Donovan Johnson, <a href="/A117349/b117349.txt">Table of n, a(n) for n = 1..180</a> (terms <= 10^12)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect Number</a>
%F sigma(n) = k*n + r, abs(r) <= log(n).
%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, A117347, A117348, A117350.
%K nonn
%O 1,1
%A _Walter Nissen_, Mar 09 2006
%E Offset corrected by _Donovan Johnson_, Oct 01 2012
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