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A117350 Near-multiperfects with primes, powers of 2, 6 * prime and 2^n * prime excluded, abs(sigma(n) mod n) <= log(n). 5
70, 110, 120, 650, 672, 884, 1155, 4030, 5830, 8925, 11096, 17816, 18632, 18904, 30240, 32445, 32760, 45356, 70564, 77744, 85936, 91388, 100804, 116624, 244036, 254012, 388076, 391612, 430272, 442365, 523776, 1090912, 1848964, 2178540 (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
Donovan Johnson, Table of n, a(n) for n = 1..114 (terms <= 10^12)
Eric Weisstein's World of Mathematics, Multiperfect Number.
EXAMPLE
70 is in the sequence because sigma(70) = 144 = 2*70 + 4, while 4 < log(70) ~= 4.248.
The 2-perfect numbers are excluded because they are 2^n * prime.
CROSSREFS
Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117346 through A117349.
Sequence in context: A043222 A039399 A044002 * A004239 A357670 A185817
KEYWORD
nonn
AUTHOR
Walter Nissen, Mar 09 2006
EXTENSIONS
Offset corrected by Donovan Johnson, Oct 01 2012
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)