A117346 Near-multiperfects: numbers m such that abs(sigma(m) mod m) <= log(m).

1, 3, 4, 5, 6, 7, 8, 10, 11, 13, 16, 17, 19, 20, 23, 28, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 64, 67, 70, 71, 73, 79, 83, 88, 89, 97, 101, 103, 104, 107, 109, 110, 113, 120, 127, 128, 131, 136, 137, 139, 149, 151, 152, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

Offset

1,2

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

Eric Weisstein's World of Mathematics, Multiperfect Number.

Example

70 is in the sequence because sigma(70) = 144 = 2*70 + 4, while 4 < log(70) ~= 4.248.

Mathematica

asmlQ[n_]:=Module[{p=Mod[DivisorSigma[1, n], n]}, If[p>n/2, p=n-p]; p<=Log[n]];
Select[Range[200], asmlQ] (* Harvey P. Dale, Dec 25 2013 *)

Crossrefs

Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117347 through A117350.

Sequence in context: A026427 A026482 A232803 * A158648 A039078 A073632

Adjacent sequences: A117343 A117344 A117345 * A117347 A117348 A117349

Keyword

nonn

Author

Walter Nissen, Mar 09 2006

Extensions

First term prepended by Harvey P. Dale, Dec 25 2013

Status

approved