8311
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 8312
- Proper Divisor Sum (Aliquot Sum)
- 1
- 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
- 8310
- Möbius Function
- -1
- Radical
- 8311
- Omega Function (Ω)
- 1
- Little Omega Function (ω)
- 1
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
- 65
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1043
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- a(0) = 0, a(1) = 1; for n >= 2, a(n) = 9*a(n-1) + 7*a(n-2).at n=5A015583
- a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (composite numbers).at n=30A024588
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (Lucas numbers), t = (odd natural numbers).at n=19A025093
- a(n) = Sum_{k=0..n} (k+1) * A026780(n, k).at n=9A027251
- Primes such that in p^2 the parity of digits alternates.at n=39A030145
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 91.at n=3A031589
- Number of bracelets (turnover necklaces) of n beads of 2 colors, 5 of them black.at n=35A032279
- Number of partitions of n with equal number of parts congruent to each of 2, 3 and 4 (mod 5).at n=53A035581
- Numerators of continued fraction convergents to sqrt(59).at n=7A041102
- Numerators of continued fraction convergents to sqrt(236).at n=7A041440
- Primes of the form 30*p + 1 where p is also prime.at n=23A051646
- Primes p with the following property: let d_1, d_2, ... be the distinct digits occurring in the decimal expansion of p. Then for each d_i, dropping all the digits d_i from p produces a prime number. Leading 0's are not allowed.at n=39A057876
- Primes with 3 distinct digits that remain prime (no leading zeros allowed) after deleting all occurrences of any one of its distinct digits.at n=29A057879
- Primes p such that p^6 reversed is also prime.at n=40A059699
- a(n) = p.q in decimal notation where p = prime(n) and q is the smallest prime (A066065(n)) such that the concatenation p.q is a prime.at n=22A066064
- Primes which are the concatenation of numbers n_1, n_2, n_3, in that order, with n_1 + n_2 = n_3 (leading zeros are forbidden for nonzero n_i).at n=7A067860
- Least prime p introducing prime-difference pattern {d, 2*d, 4*d}, where d = 2*n, i.e., {p, p+2*n, p+6*n, p+14*n} are consecutive primes.at n=2A079012
- a(n) = Sum(((k-1)/2)*k!*Stirling_2(n,k),k=1..n).at n=5A083411
- Primes in which the digit string can be partitioned into three parts such that the sum of the first two is equal to the third, and the second part is nonzero.at n=6A088291
- Matrix product of Stirling2-triangle A008277(n,k) and unsigned Lah-triangle |A008297(n,k)|.at n=16A088729