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

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? Sigma is the sum_of_divisors function.

Examples

			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.
		

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.

Crossrefs

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

Extensions

Offset corrected by Donovan Johnson, Oct 01 2012