309
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 416
- Proper Divisor Sum (Aliquot Sum)
- 107
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 204
- Möbius Function
- 1
- Radical
- 309
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 2
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
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
- no
Recreational
- Happy Number
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 24
- Smith Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- 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
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- dreihundertneun· ordinal: dreihundertneunste
- English
- three hundred nine· ordinal: three hundred ninth
- Spanish
- trescientos nueve· ordinal: 309º
- French
- trois cent neuf· ordinal: trois cent neufième
- Italian
- trecentonove· ordinal: 309º
- Latin
- trecenti novem· ordinal: 309.
- Portuguese
- trezentos e nove· ordinal: 309º
Appears in sequences
- 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); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).at n=21A000223
- a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.at n=5A000255
- Triangle giving number L(n,k) of normalized k X n Latin rectangles.at n=22A001009
- Number of permutations of length n by rises.at n=1A001280
- a(1) = 1; thereafter a(n+1) = floor(sqrt(2*a(n)*(a(n)+1))).at n=15A001521
- a(1) = a(2) = 1, a(3) = 4; thereafter a(n) = a(n-1) + a(n-3).at n=14A001609
- A Fielder sequence. a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5), n >= 6.at n=10A001639
- 5th forward differences of factorial numbers A000142.at n=1A001689
- a(n) = 3 * prime(n).at n=26A001748
- Absolute value of coefficients of an elliptic function.at n=4A001940
- Number of two-rowed partitions of length 3.at n=15A001993
- Numbers k such that 9*2^k - 1 is prime.at n=12A002236
- Numerators of continued fraction convergents to fifth root of 2.at n=7A002362
- Numbers k such that (k^2 + 1)/2 is prime.at n=48A002731
- a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.at n=38A002815
- Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.at n=54A002858
- a(n) (n>6) is least integer > a(n-1) with precisely three representations a(n) = a(i) + a(j), 1 <= i < j < n, a(n) = n for n=1..6.at n=59A003045
- Coefficients in expansion of permanent of infinite tridiagonal matrix shown below.at n=34A003113
- Positions of letter c in the tribonacci word abacabaabacababac... generated by a->ab, b->ac, c->a (cf. A092782).at n=49A003146
- a(n) = a(n-1) + 2*a(n-3) with a(0)=a(1)=1, a(2)=3.at n=11A003229