A117349 - OEIS

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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

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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) really "near" a multiple of n, for n=9? Or n=18? Log is the natural logarithm. 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..180 (terms <= 10^12)

Eric Weisstein's World of Mathematics, Multiperfect Number

FORMULA

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

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.

Cf. A088007, A088008, A088009, A088010, A088011, A088012.