165
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
- 2
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 288
- Proper Divisor Sum (Aliquot Sum)
- 123
- 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
- 80
- Möbius Function
- -1
- Radical
- 165
- Omega Function (Ω)
- 3
- Little Omega Function (ω)
- 3
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
- yes
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 111
- Smith Number
- 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
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- einshundertfünfundsechzig· ordinal: einshundertfünfundsechzigste
- English
- one hundred sixty-five· ordinal: one hundred sixty-fifth
- Spanish
- ciento sesenta y cinco· ordinal: 165º
- French
- cent soixante-cinq· ordinal: cent soixante-cinqième
- Italian
- centosessantacinque· ordinal: 165º
- Latin
- centum sexaginta quinque· ordinal: 165.
- Portuguese
- cento e sessenta e cinco· ordinal: 165º
Appears in sequences
- Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.at n=26A000009
- Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.at n=9A000292
- a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.at n=5A000447
- a(n) = binomial coefficient C(n,8).at n=3A000581
- Number of compositions of n into 3 ordered relatively prime parts.at n=21A000741
- Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers).at n=42A000926
- Genus of complete graph on n nodes.at n=47A000933
- Numbers that are divisible by at least three different primes.at n=21A000977
- a(n) is the solution to the postage stamp problem with 4 denominations and n stamps.at n=6A001209
- Triangle read by rows, in which row n consists of n(n+m) for m = 1 .. n-1.at n=48A001283
- Numbers of form m*k with m+1 <= k <= 2m-1.at n=45A001284
- Number of graphs with n nodes and n-3 edges.at n=9A001431
- Numbers k such that 19*2^k - 1 is prime.at n=9A001775
- Expansion of g.f. x/((1 - x)^2*(1 - x^3)).at n=30A001840
- Sorting numbers: maximal number of comparisons for sorting n elements by binary insertion.at n=37A001855
- a(1)=2, a(2)=3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.at n=36A001857
- Number of n-bead necklaces with 5 colors.at n=4A001869
- Denominators of cosecant numbers: -2*(2^(2*n-1)-1)*Bernoulli(2*n).at n=10A001897
- a(n) = floor((n+1/2)*(2+sqrt(2))); winning positions in the 2-Wythoff game.at n=48A001954
- Segmented numbers, or prime numbers of measurement.at n=62A002048