From Wikipedia, the free encyclopedia
Natural number
135 (one hundred [and] thirty-five) is the
natural number following
134 and preceding
136.
In mathematics
135 is the number of
integer partitions of
14, and the number of rooted trees with
15 nodes and height at most 2.
[1] 135 is 5-
smooth, since its prime factorization is , and a
Harshad number in
decimal.
[2]
[3]
Using its own digits, 135 in
base-10 can be expressed in operations as the sum of consecutive powers of its digits, and as a
sum-product number:
-
[4]
-
[5]
135 is the number of degrees in the
internal angle of a regular eight-sided
octagon, and the number of
nodes inside a regular
nonagon from the intersection of its
diagonals and
sides.
[6] Also:
While the central angle of a regular octagon is 135 ÷ 3 = 45 degrees, 4.5 is the
harmonic mean of all eight divisors of 135.
The
aliquot sum of 135 is
105, which is the 14th
triangular number, or equivalently the sum of the first fourteen non-zero positive
integers.
[8]
[9]
There are 135 total Krotenheerdt
k-uniform tilings for k < 8, with no other such tilings for higher k.
[10]
There are a total of 135
primes between
1,000 and
2,000.
for is a
polynomial that plays an essential role in
Apéry's proof that is irrational.[
citation needed]
In other fields
See also
References
-
^
Sloane, N. J. A. (ed.).
"Sequence A000041 (The number of partitions of n (the partition numbers))". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-05.
-
^
Sloane, N. J. A. (ed.).
"Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-05.
-
^
Sloane, N. J. A. (ed.).
"Sequence A051037 (5-smooth numbers, i.e., numbers whose prime divisors are all less than or equal to five.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-05.
-
^
"Sloane's A032799: Numbers n such that n equals the sum of its digits raised to the consecutive powers (1,2,3,...)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2019-12-08.
-
^
"Sloane's A038369 : Numbers n such that n = (product of digits of n) * (sum of digits of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
-
^
Sloane, N. J. A. (ed.).
"Sequence A007569 (Number of nodes in regular n-gon with all diagonals drawn.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-04.
-
^
Sloane, N. J. A. (ed.).
"Sequence A000010 (Euler totient function phi(n): count numbers less than or equal to n and prime to n.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-06.
-
^
Sloane, N. J. A. (ed.).
"Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-06.
-
^
Sloane, N. J. A. (ed.).
"Sequence A000217 (Triangular numbers)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-06.
-
^
Sloane, N. J. A. (ed.).
"Sequence A068600 (Number of n-uniform tilings having n different arrangements of polygons about their vertices.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-09.
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100,000
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1,000,000
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10,000,000
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100,000,000
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1,000,000,000
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