A117348 Near-multiperfects with primes and powers of 2 excluded, abs(sigma(m) mod m) <= log(m).

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? Sigma is the sum_of_divisors function.

References

R. K. Guy, Unsolved Problems in Number Theory, B2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

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

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

Cf. A117346, A117347, A117349, A117350.

Sequence in context: A169810 A095146 A163172 * A117349 A362183 A153369

Adjacent sequences: A117345 A117346 A117347 * A117349 A117350 A117351

Keyword

nonn

Author

Walter Nissen, Mar 09 2006

Extensions

Offset corrected by Amiram Eldar, Mar 05 2020

Status

approved