A045769 -id:A045769 - cp's OEIS frontend

A117348 Near-multiperfects with primes and powers of 2 excluded, abs(sigma(m) mod m) <= log(m).

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

Walter Nissen, Mar 09 2006

nonn

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.

			70 is a term because sigma(70) = 144 = 2 * 70 + 4, while 4 < log (70) ~= 4.248.

R. K. Guy, Unsolved Problems in Number Theory, B2.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Walter Nissen, Near Multiperfects.
Eric Weisstein's World of Mathematics, Multiperfect Number

Cf. A045768, A045769, A045770, A077374, A087167, A087485.
Cf. A088007, A088008, A088010, A088011, A088012.
Cf. A117346, A117347, A117349, A117350.

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

Offset corrected by Amiram Eldar, Mar 05 2020

A181704 Numbers m=2^(t-1)*(2^t-5), where 2^t-5 is prime.

Original entry on oeis.org

12, 88, 1888, 32128, 521728, 8378368, 34359083008, 549753192448, 2251799645913088, 9223372026117357568, 2361183241263023915008, 2596148429267413634121263069790208, 2722258935367507707522529418717050175488

Offset: 1

Vladimir Shevelev, Nov 06 2010

nonn

All these numbers are in A181595 because their abundance is 4, a proper divisor of m.

Cf. A059608, A156560, A181595, A181701, A000396, A181703, A045769

Rest[2^(#-1) (2^#-5)&/@(Round[N[Log[#+5]/Log[2]]]&/@Select[Table[2^t-5,{t,120}],PrimeQ])] (* Harvey P. Dale, Dec 16 2010 *)

571728 replaced with 521728 by R. J. Mathar, Dec 05 2010

cp's OEIS Frontend

A117348 Near-multiperfects with primes and powers of 2 excluded, abs(sigma(m) mod m) <= log(m).

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