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 A117347 #26 Feb 16 2025 08:33:00 %S A117347 4,6,8,10,16,20,28,32,64,70,88,104,110,120,128,136,152,256,464,496, %T A117347 512,592,650,672,884,1024,1155,1888,1952,2048,2144,4030,4096,5830, %U A117347 8128,8192,8384,8925,11096,16384,17816,18632,18904,30240,32128,32445,32760,32768 %N A117347 Near-multiperfects with primes excluded, abs(sigma(m) mod m) <= log(m). %C A117347 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 A117347 R. K. Guy, Unsolved Problems in Number Theory, B2. %H A117347 Amiram Eldar, <a href="/A117347/b117347.txt">Table of n, a(n) for n = 1..10000</a> %H A117347 Walter Nissen, <a href="http://upforthecount.com/math/nearmpf.html">Near Multiperfects</a>. %H A117347 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect Number</a> %F A117347 sigma(m) = k * m + r, abs(r) <= log(m). %e A117347 70 is a term because sigma(70) = 144 = 2 * 70 + 4, while 4 < log(70) ~= 4.248. %Y A117347 Cf. A045768, A045769, A045770, A077374, A087167, A087485. %Y A117347 Cf. A088007, A088008, A088009, A088010, A088011, A088012. %Y A117347 Cf. A117346, A117348, A117349, A117350. %K A117347 nonn %O A117347 1,1 %A A117347 _Walter Nissen_, Mar 09 2006 %E A117347 Offset corrected by _Amiram Eldar_, Mar 05 2020