A117346 - OEIS

%I #46 Feb 16 2025 08:33:00

%S 1,3,4,5,6,7,8,10,11,13,16,17,19,20,23,28,29,31,32,37,41,43,47,53,59,

%T 61,64,67,70,71,73,79,83,88,89,97,101,103,104,107,109,110,113,120,127,

%U 128,131,136,137,139,149,151,152,157,163,167,173,179,181,191,193,197,199

%N Near-multiperfects: numbers m such that 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) really "near" a multiple of n, for n=9? Or n=18? Sigma is the sum_of_divisors function.

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

%H Amiram Eldar, <a href="/A117346/b117346.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t asmlQ[n_]:=Module[{p=Mod[DivisorSigma[1,n],n]},If[p>n/2,p=n-p];p<=Log[n]];

%t Select[Range[200],asmlQ] (* _Harvey P. Dale_, Dec 25 2013 *)

%Y Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117347 through A117350.

%K nonn

%O 1,2

%A _Walter Nissen_, Mar 09 2006

%E First term prepended by _Harvey P. Dale_, Dec 25 2013