This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117349 #22 Feb 16 2025 08:33:00 %S A117349 6,10,20,28,70,88,104,110,120,136,152,464,496,592,650,672,884,1155, %T A117349 1888,1952,2144,4030,5830,8128,8384,8925,11096,17816,18632,18904, %U A117349 30240,32128,32445,32760,32896,33664,45356,70564,77744,85936,91388,100804,116624 %N A117349 Near-multiperfects with primes, powers of 2 and 6 * prime excluded, abs(sigma(n) mod n) <= log(n). %C A117349 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 A117349 R. K. Guy, Unsolved Problems in Number Theory, B2. %H A117349 Donovan Johnson, <a href="/A117349/b117349.txt">Table of n, a(n) for n = 1..180</a> (terms <= 10^12) %H A117349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect Number</a> %F A117349 sigma(n) = k*n + r, abs(r) <= log(n). %e A117349 70 is a term because sigma(70) = 144 = 2*70 + 4, while 4 < log(70) ~= 4.248. %Y A117349 Cf. A045768, A045769, A045770, A077374, A087167, A087485. %Y A117349 Cf. A088007, A088008, A088009, A088010, A088011, A088012. %Y A117349 Cf. A117346, A117347, A117348, A117350. %K A117349 nonn %O A117349 1,1 %A A117349 _Walter Nissen_, Mar 09 2006 %E A117349 Offset corrected by _Donovan Johnson_, Oct 01 2012