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

Author

Walter Nissen, Mar 09 2006

Keywords

• nonn

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?

Examples

			70 is a term because sigma(70) = 144 = 2 * 70 + 4, while 4 < log(70) ~= 4.248.
		

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

Crossrefs

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

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

Cf. A117346, A117348, A117349, A117350.

Formula

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

Extensions

Offset corrected by Amiram Eldar, Mar 05 2020