Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #26 Apr 23 2023 07:30:02
%S 70,110,120,650,672,884,1155,4030,5830,8925,11096,17816,18632,18904,
%T 30240,32445,32760,45356,70564,77744,85936,91388,100804,116624,244036,
%U 254012,388076,391612,430272,442365,523776,1090912,1848964,2178540
%N Near-multiperfects with primes, powers of 2, 6 * prime and 2^n * 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? Sigma is the sum_of_divisors function.
%D R. K. Guy, Unsolved Problems in Number Theory, B2.
%H Donovan Johnson, <a href="/A117350/b117350.txt">Table of n, a(n) for n = 1..114</a> (terms <= 10^12)
%H Eric Weisstein's World of Mathematics, <a href="http://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.
%e The 2-perfect numbers are excluded because they are 2^n * prime.
%Y Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117346 through A117349.
%K nonn
%O 1,1
%A _Walter Nissen_, Mar 09 2006
%E Offset corrected by _Donovan Johnson_, Oct 01 2012