A117347 - OEIS

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

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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.