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A117348 Near-multiperfects with primes and powers of 2 excluded, abs(sigma(m) mod m) <= log(m). 3
6, 10, 20, 28, 70, 88, 104, 110, 120, 136, 152, 464, 496, 592, 650, 672, 884, 1155, 1888, 1952, 2144, 4030, 5830, 8128, 8384, 8925, 11096, 17816, 18632, 18904, 30240, 32128, 32445, 32760, 32896, 33664, 45356, 70564, 77744, 85936, 91388, 100804, 116624 (list; graph; refs; listen; history; text; internal format)
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? Sigma is the sum_of_divisors function.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B2.
LINKS
Walter Nissen, Near Multiperfects.
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
Sequence in context: A169810 A095146 A163172 * A117349 A362183 A153369
KEYWORD
nonn
AUTHOR
Walter Nissen, Mar 09 2006
EXTENSIONS
Offset corrected by Amiram Eldar, Mar 05 2020
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)