7105
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
- 1
Divisibility
- Divisor Count
- 12
- Divisor Sum
- 10260
- Proper Divisor Sum (Aliquot Sum)
- 3155
- 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
- 4704
- Möbius Function
- 0
- Radical
- 1015
- Omega Function (Ω)
- 4
- 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
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 57
- Smith Number
- no
- Vampire 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
- no
- Odd
- yes
Appears in sequences
- a(n) = (n + 3)*(n^2 + 6*n + 2)/6.at n=32A005286
- Number of permutations of [n] with four inversions.at n=16A005287
- Number of n-bead bracelets (turnover necklaces) with 12 red beads.at n=9A005516
- Expansion of e.g.f.: sec(exp(x)-sec(x))=1+1/2!*x^2+9/4!*x^4-20/5!*x^5+177/6!*x^6...at n=8A013338
- Odd octagonal numbers: (2n+1)*(6n+1).at n=24A014641
- a(n) = dot_product(1,2,...,n)*(5,6,...,n,1,2,3,4).at n=24A026043
- Number of bracelets (turnover necklaces) of n beads of 2 colors, 9 of them black.at n=12A032281
- Numbers whose set of base-12 digits is {1,4}.at n=24A032824
- Positive numbers having the same set of digits in base 8 and base 10.at n=30A037442
- Number of primes between n*100000 and (n+1)*100000.at n=13A038825
- Expansion of (1-x)/(1 - 4*x + x^2 + x^3).at n=7A052941
- Number of symmetric types of (3,2n)-hypergraphs under action of complementing group C(3,2).at n=27A055780
- Dimension of the space of weight n cuspidal newforms for Gamma_1( 71 ).at n=34A063344
- Composite numbers k with no prime factor among (2, 3) (cf. A038509) and such that phi(k) < 2*k/3.at n=23A069043
- Triangle of T1(n,m) = number of bracelets (necklaces that can be turned over) with m white beads and (2n+1-m) black ones, for 1<=m<=n.at n=53A078925
- Triangle read by rows: T(n,k), n >=1, 0 <= k <= C(n,k), = number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and 1's and 0's elsewhere and with k 1's above the diagonal.at n=87A083029
- Molien series for group of order 4608 acting on joint weight enumerators of a pair of binary doubly-even self-dual codes.at n=36A097870
- a(1) = 668; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).at n=26A105212
- Number of partitions of {1...n} containing 3 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly three 2-strings.at n=4A105489
- Number of partitions of {1...n} containing 4 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly four 2-strings.at n=3A105490