OFFSET
1,1
COMMENTS
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.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B2.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..180 (terms <= 10^12)
Eric Weisstein's World of Mathematics, Multiperfect Number
FORMULA
sigma(n) = k*n + r, abs(r) <= log(n).
EXAMPLE
70 is a term because sigma(70) = 144 = 2*70 + 4, while 4 < log(70) ~= 4.248.
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Nissen, Mar 09 2006
EXTENSIONS
Offset corrected by Donovan Johnson, Oct 01 2012
STATUS
approved