680
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 14
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 16
- Divisor Sum
- 1620
- Proper Divisor Sum (Aliquot Sum)
- 940
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 256
- Möbius Function
- 0
- Radical
- 170
- Omega Function (Ω)
- 5
- 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
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 12
- Smith Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- 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
- yes
- Odd
- no
Names
- German
- sechshundertachtzig· ordinal: sechshundertachtzigste
- English
- six hundred eighty· ordinal: six hundred eightieth
- Spanish
- seiscientos ochenta· ordinal: 680º
- French
- six cent quatre-vingts· ordinal: six cent quatre-vingtsième
- Italian
- seicentoottanta· ordinal: 680º
- Latin
- sescenti octoginta· ordinal: 680.
- Portuguese
- seiscentos e oitenta· ordinal: 680º
Appears in sequences
- Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.at n=15A000292
- a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.at n=8A000447
- Number of partially labeled trees with n nodes (4 of which are labeled).at n=2A000485
- Number of permutations of length n by rises.at n=2A001279
- Expansion of 1/((1-x)^2*(1-x^2)*(1-x^5)).at n=30A001304
- Numbers in which every digit contains at least one loop (version 1).at n=24A001743
- Number of integral points in a certain sequence of closed quadrilaterals.at n=38A002579
- Number of unrooted triangulations of a disk that have reflection symmetry with n interior nodes and 3 nodes on the boundary.at n=8A002712
- Beginnings of periodic unitary aliquot sequences.at n=54A003062
- Numbers that are the sum of 10 positive 5th powers.at n=27A003355
- Numbers of edges of regular polygons constructible with ruler (or, more precisely, an unmarked straightedge) and compass.at n=49A003401
- Degrees of irreducible representations of Held group He.at n=5A003912
- Expansion of (1-x+x^2)/((1-x)^2*(1-x^2)*(1-x^4)).at n=29A005232
- Erroneous version of A033678.at n=5A005780
- Number of asymmetric planted projective plane trees with n+1 nodes; bracelets (reversible necklaces) with n black beads and n-1 white beads.at n=8A006079
- Numbers k such that k^8 + 1 is prime.at n=26A006314
- Total preorders.at n=4A006326
- Binomial coefficients: C(n,k), 2 <= k <= n-2, sorted, duplicates removed.at n=50A006987
- a(n) = phi(n) * (sigma(n) - n).at n=54A007517
- Numbers that are the sum of 2 nonzero squares in 2 or more ways.at n=44A007692