A117349 Near-multiperfects with primes, powers of 2 and 6 * prime excluded, abs(sigma(n) mod n) <= log(n).

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

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

Cf. A045768, A045769, A045770, A077374, A087167, A087485.

Cf. A088007, A088008, A088009, A088010, A088011, A088012.

Cf. A117346, A117347, A117348, A117350.

Sequence in context: A095146 A163172 A117348 * A362183 A153369 A107981

Adjacent sequences: A117346 A117347 A117348 * A117350 A117351 A117352

Keyword

nonn

Author

Walter Nissen, Mar 09 2006

Extensions

Offset corrected by Donovan Johnson, Oct 01 2012

Status

approved