A117347 Near-multiperfects with primes excluded, abs(sigma(m) mod m) <= log(m).

4, 6, 8, 10, 16, 20, 28, 32, 64, 70, 88, 104, 110, 120, 128, 136, 152, 256, 464, 496, 512, 592, 650, 672, 884, 1024, 1155, 1888, 1952, 2048, 2144, 4030, 4096, 5830, 8128, 8192, 8384, 8925, 11096, 16384, 17816, 18632, 18904, 30240, 32128, 32445, 32760, 32768

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) (where sigma is the sum-of-divisors function) really "near" a multiple of n, for n = 9? Or n = 18?

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(m) = k * m + r, abs(r) <= log(m).

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, A117348, A117349, A117350.

Sequence in context: A062711 A280739 A353917 * A088011 A289424 A050835

Adjacent sequences: A117344 A117345 A117346 * A117348 A117349 A117350

Keyword

nonn

Author

Walter Nissen, Mar 09 2006

Extensions

Offset corrected by Amiram Eldar, Mar 05 2020

Status

approved