836 (eight hundred
ndthirty-six) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
835 and preceding
837
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Year 837 ( DCCCXXXVII) was a common year starting on Monday of the Julian calendar.
Events
By place Byzantine Empire
* Byzantine–Arab War: Emperor Theophilos leads a massive Byzantine expeditionary force into Mesopotamia. ...
.
In mathematics
The factorization of 836 is , so its proper factors are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, and 418. They sum to 844. As this is greater than 836, it is an
abundant number
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total ...
, but no subset sums to 836, so it is not a
semiperfect number; therefore it is a
weird number.
Besides, 836 is the smallest weird number that is also an
untouchable number, i.e. there is no ''n'' such that the sum of proper factors of ''n'' equals 836. (The only smaller weird number
70 is not untouchable, since σ(134) − 134 = 70)
See also
*
836 (year)
*
836 Jole (asteroid)
*
836th Air Division, an inactive United States Air Force organization
*
836 Naval Air Squadron, a World War II organization in the British Navy
*
Pi Arietis, designated as object 836 in the Bright Star catalogue
References
Integers
{{Num-stub