30
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 3
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 72
- Proper Divisor Sum (Aliquot Sum)
- 42
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- yes
Derived Values
- Euler's Totient
- 8
- Möbius Function
- -1
- Radical
- 30
- Omega Function (Ω)
- 3
- Little Omega Function (ω)
- 3
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- yes
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- yes
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 18
- Smith Number
- no
Classification
- Natural
- yes
- Even
- yes
- Odd
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- yes
- Carmichael Number
- no
Names
- German
- dreißig· ordinal: dreißigste
- English
- thirty· ordinal: thirtieth
- Spanish
- treinta· ordinal: 30º
- French
- trente· ordinal: trentième
- Italian
- trenta· ordinal: 30º
- Latin
- triginta· ordinal: 30.
- Portuguese
- trinta· ordinal: 30º
Appears in sequences
- Euler totient function phi(n): count numbers <= n and prime to n.at n=30A000010
- Euler totient function phi(n): count numbers <= n and prime to n.at n=61A000010
- Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed.at n=9A000013
- a(n) is the number of distinct (infinite) output sequences from binary n-stage shift register which feeds back the complement of the last stage.at n=9A000016
- Number of positive integers <= 2^n of form x^2 + 12 y^2.at n=7A000021
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=29A000026
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=39A000026
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=44A000026
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=29A000027
- Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.at n=15A000028
- Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets).at n=8A000029
- Numbers that are not squares (or, the nonsquares).at n=24A000037
- a(n) is the number of partitions of n (the partition numbers).at n=9A000041
- Generalized tangent numbers d(n,1).at n=17A000061
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=21A000062
- Smallest number of vertices in trivalent graph with girth (shortest cycle) = n.at n=5A000066
- a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).at n=6A000070
- a(n) = n^2*Product_{p|n} (1 + 1/p).at n=4A000082
- Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.at n=7A000092
- 2nd power of rooted tree enumerator; number of linear forests of 2 rooted trees.at n=4A000106