A117349 Near-multiperfects with primes, powers of 2 and 6 * prime excluded, abs(sigma(n) mod n) <= log(n).

6, 10, 20, 28, 70, 88, 104, 110, 120, 136, 152, 464, 496, 592, 650, 672, 884, 1155, 1888, 1952, 2144, 4030, 5830, 8128, 8384, 8925, 11096, 17816, 18632, 18904, 30240, 32128, 32445, 32760, 32896, 33664, 45356, 70564, 77744, 85936, 91388, 100804, 116624

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) really "near" a multiple of n, for n=9? Or n=18? Log is the natural logarithm. Sigma is the sum_of_divisors function.

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

• Donovan Johnson, Table of n, a(n) for n = 1..180 (terms <= 10^12)
• 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, A117347, A117348, A117350.

Formula

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

Extensions

Offset corrected by Donovan Johnson, Oct 01 2012