7687
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 28
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 7688
- 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
- 7686
- Möbius Function
- -1
- Radical
- 7687
- 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
- 57
- 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
- 975
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Expansion of Product_{m>=1} 1/(1 - m*q^m)^6.at n=6A022730
- Least k>1 such that reverse of first n terms of A006928 repeats beginning at k-th term.at n=52A025509
- Least k>1 such that reverse of first n terms of A022303 repeats beginning at k-th term.at n=46A025520
- a(n) = (1/s(1) + 1/s(2) + ... + 1/s(n+1)) * LCM{1, 2, ..., n}, where s(k) = LCM{1,2,...,k}/k = A002944(k).at n=9A025537
- a(n) = (d(n)-r(n))/2, where d = A026060 and r is the periodic sequence with fundamental period (1,0,0,0).at n=36A026061
- 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 87.at n=12A031585
- Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 54 ones.at n=16A031822
- Numerators of continued fraction convergents to sqrt(427).at n=7A041812
- Numerators of continued fraction convergents to sqrt(679).at n=4A042304
- First differences are A005563.at n=27A047732
- Primes whose sum of digits is the perfect number 28.at n=13A048517
- Primes p such that x^61 = 2 has no solution mod p.at n=16A059230
- Primes p such that p^8 reversed is also prime.at n=40A059701
- Irregular primes with irregularity index three.at n=13A060975
- Primes starting and ending with 7.at n=25A062334
- a(n) is the smallest prime m such that prod(m) = n*length(m)*sum(m) where prod(m) is the product of the digits of m, length(m) is the number of digits of m, sum(m) is the sum of the digits of m; or 0 if no such m exists.at n=20A064023
- Permutation of N induced by rotating the node 7 left in the infinite planar binary tree shown at A065658.at n=59A065673
- Primes of the form 2*n^2 - 1.at n=31A066436
- a(1) = 1; a(2n) is the smallest prime == 1 mod (a(2n-1)) and a(2n+1) is the smallest composite number == 1 (mod a(2n)).at n=17A075340
- a(1) = 1, a(2n) is the smallest composite number == 1 mod (a(2n-1)) and a(2n+1) is the smallest prime == 1 (mod a(2n)).at n=22A075341