413
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 8
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 480
- Proper Divisor Sum (Aliquot Sum)
- 67
- 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
- 348
- Möbius Function
- 1
- Radical
- 413
- 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
- 89
- 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
- vierhundertdreizehn· ordinal: vierhundertdreizehnste
- English
- four hundred thirteen· ordinal: four hundred thirteenth
- Spanish
- cuatrocientos trece· ordinal: 413º
- French
- quatre cent treize· ordinal: quatre cent treizième
- Italian
- quattrocentotredici· ordinal: 413º
- Latin
- quadringenti tredecim· ordinal: 413.
- Portuguese
- quatrocentos e treze· ordinal: 413º
Appears in sequences
- Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents.at n=54A000008
- Rao Uppuluri-Carpenter numbers (or complementary Bell numbers): e.g.f. = exp(1 - exp(x)).at n=10A000587
- Number of partitions of n into prime parts.at n=43A000607
- Numbers beginning with letter 'f' in English.at n=37A000867
- Number of plane partitions of n with at most two rows.at n=12A000990
- Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^7 in powers of x.at n=26A001485
- Prime numbers of measurement.at n=19A002049
- Number of partitions of n with exactly two part sizes.at n=58A002133
- Take solution to Pellian equation x^2 - n*y^2 = 1 with smallest positive y and x >= 0; sequence gives a(n) = y, or 0 if n is a square. A002350 gives values of x.at n=70A002349
- Numbers k such that binomial(2*k,k) is divisible by (k+1)^2.at n=34A002503
- Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).at n=44A003052
- Numbers of the form 8k+5; or, numbers whose binary expansion ends in 101.at n=51A004770
- a(n) = round(n*phi^6), where phi is the golden ratio, A001622.at n=23A004941
- a(n) = ceiling(n*phi^6), where phi is the golden ratio.at n=23A004961
- Expansion of (1-x+x^2)/((1-x)^2*(1-x^2)*(1-x^4)).at n=24A005232
- Positions of remoteness 4 in Beans-Don't-Talk.at n=12A005696
- a(n) = a(n-1) + a(n-7), with a(i) = 1 for i = 0..6.at n=30A005709
- Quadrinomial coefficients.at n=5A005719
- Related to series-parallel networks.at n=5A006349
- Number of binary vectors of length n+1 beginning with 0 and containing just 1 singleton.at n=12A006367