A117350 Near-multiperfects with primes, powers of 2, 6 * prime and 2^n * prime excluded, abs(sigma(n) mod n) <= log(n).

70, 110, 120, 650, 672, 884, 1155, 4030, 5830, 8925, 11096, 17816, 18632, 18904, 30240, 32445, 32760, 45356, 70564, 77744, 85936, 91388, 100804, 116624, 244036, 254012, 388076, 391612, 430272, 442365, 523776, 1090912, 1848964, 2178540

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

Donovan Johnson, Table of n, a(n) for n = 1..114 (terms <= 10^12)

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.
The 2-perfect numbers are excluded because they are 2^n * prime.

Crossrefs

Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117346 through A117349.

Sequence in context: A043222 A039399 A044002 * A004239 A357670 A185817

Adjacent sequences: A117347 A117348 A117349 * A117351 A117352 A117353

Keyword

nonn

Author

Walter Nissen, Mar 09 2006

Extensions

Offset corrected by Donovan Johnson, Oct 01 2012

Status

approved