10103
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 5
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 10104
- 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
- 10102
- Möbius Function
- -1
- Radical
- 10103
- 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
- 86
- 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
- yes
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1241
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).at n=41A001994
- From table of maximal epacts e(p) and corresponding primes p, for x_1=2, x_{m+1} = (x_m)^2+1; sequence gives p.at n=30A014424
- Fibonacci sequence beginning 2 9.at n=16A022114
- Primes of form n^2 + n + 3.at n=14A027753
- 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 99.at n=27A031597
- Numbers whose base-10 representation has exactly 5 runs.at n=2A043641
- Primes associated with A052507.at n=33A052480
- Numbers n such that sum of digits = number of digits.at n=34A061384
- Primes whose sum of digits is 5.at n=15A062341
- Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 1.at n=4A068166
- Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 3.at n=4A068168
- Smallest n-digit prime with property that digits alternate in parity.at n=4A068876
- Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).at n=5A069710
- Smallest n-digit prime with digit sum n, or 0 if no such prime exists.at n=4A073864
- Duplicate of A069710.at n=5A073903
- First prime after phi(prime(n)^2).at n=25A079477
- 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=29A080437
- Prime numbers such that first reversing digits and after squaring equals the result of first-squaring and after-reversing. Primes in A085305.at n=20A085306
- Primes whose decimal representation is a valid number in base 5 and interpreted as such is again a prime.at n=19A090708
- Primes in A051022.at n=21A092908