10337
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 14
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 10338
- Proper Divisor Sum (Aliquot Sum)
- 1
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 10336
- Möbius Function
- -1
- Radical
- 10337
- 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
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 148
- 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
- 1269
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Number of ways to pair up {1^2, 2^2, ..., (2n)^2 } so sum of each pair is prime.at n=11A000348
- Numbers k such that the continued fraction for sqrt(k) has period 39.at n=16A020378
- Positive numbers k such that k and 7*k are anagrams in base 8 (written in base 8).at n=2A023078
- Third term of weak prime quintets: p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).at n=23A054825
- Primes p such that x^16 = 2 has no solution mod p, but x^8 = 2 has a solution mod p.at n=19A059287
- Primes p such that x^48 = 2 has no solution mod p, but x^24 = 2 has a solution mod p.at n=15A059669
- Primes p such that x^8 = 2 has a solution mod p, but x^(8^2) = 2 has no solution mod p.at n=24A070184
- For n < 5, a(n) = n-th prime. For n >= 5, let m = n-th prime. If m is a k-digit prime then a(n) = smallest prime obtained by inserting at least one digit between every pair of digits of m. There are (k-1) places where digit insertion takes place and a(n) contains at least 2k-1 digits.at n=32A080437
- Primes which are the sum of three positive 4th powers.at n=21A085318
- Smallest prime with n prime substrings (excluding prime itself but allowing leading zeros).at n=9A085822
- a(1)=2; for n>1 a(n) is the largest prime number m such that a(n-1)^(1/(n-1))>m^(1/n).at n=21A086566
- Convolution of sequence of primes with sequence sigma(n).at n=22A086718
- Beginning with 2, smallest primes such that a(k)-a(k-1) is a distinct power of 2.at n=8A087356
- a(n) = smallest k such that the Reverse and Add! trajectory of A063048(n) joins the trajectory of k.at n=22A089493
- Primes of the form 6*p - 1 such that p and 6*p - 5 are primes.at n=39A090609
- Primes of the form 64n+33.at n=36A105128
- Integers 1 through n written in primorial base, summed as if decimal.at n=31A122613
- Prime numbers that are the sum of three distinct positive fourth powers.at n=10A126657
- Prime numbers appearing in A139033.at n=6A139034
- Primes of the form 41+(n+n^2)/2=41+A000217(n).at n=22A139219