8161
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 16
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 8162
- 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
- 8160
- Möbius Function
- -1
- Radical
- 8161
- 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
- 176
- 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
- 1024
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Primes p == 1 (mod 8), p = a^2 +64*b^2 such that y^2 = x^3 + p*x has rank 0.at n=40A007765
- a(n) = prime(n^2).at n=31A011757
- Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 46 ones.at n=25A031814
- a(n) = prime(2^n).at n=10A033844
- Primes with first digit 8.at n=33A045714
- Third term of strong prime 5-tuples: p(m-1)-p(m-2) > p(m)-p(m-1) > p(m+1)-p(m) > p(m+2)-p(m+1).at n=23A054810
- Primes p for which the period of reciprocal = (p-1)/8.at n=15A056213
- Expansion of series related to Liouville's Last Theorem: g.f. sum_{t>0} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^5 *product_{i=1..t} (1-x^i) ).at n=14A059822
- Integer part of (Product(n^((1 + log(i))/i^2), {i, 1, n})).at n=40A062482
- pi(n) is a power of 2, where pi(n) = A000720(n) is the number of primes <= n.at n=37A073798
- Numbers that begin a run of consecutive integers k such that PrimePi(k) divides 2^k.at n=9A073799
- Octo numbers (a polygonal sequence): a(n) = 5*n^2 - 6*n + 2 = (n-1)^2 + (2*n-1)^2.at n=40A079273
- Primes which are 1 mod m, where m is the index of the prime in sequence A002313 (Real primes with corresponding complex primes). The index m can be found in A084166 Primes which are -1 mod m can be found in sequence A084163.at n=12A084165
- Gregorian calendar years with Ascension Day in April.at n=33A084427
- Smallest prime of the form concatenation n, 2n, 3n,...kn and 1.at n=7A090921
- a(n) is the smallest positive integer such that the product of all 1/(1-1/a(n)) is less than e, the base of natural logarithms.at n=3A092389
- a(n) = prime(4^prime(n)).at n=2A096325
- Prime(p^10) where p is the n-th prime.at n=0A096329
- Largest prime which can be formed from digits of n^2, or 0, if no prime.at n=40A102600
- Primes from merging of 4 successive digits in decimal expansion of cos(1).at n=38A104960