Properties of the Number 67957

Sixty-Seven Thousand Nine Hundred Fifty-Seven

Basics

Value: 67956 → 67957 → 67958

Parity: odd

Prime: Yes

Previous Prime: 67943

Next Prime: 67961

Digit Sum: 34

Digital Root: 7

Palindrome: No

Factorization: 67957

Divisors: 1, 67957

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 10000100101110101

Octal: 204565

Duodecimal: 333B1

Hexadecimal: 10975

Square: 4618153849

Square Root: 260.6856344335069

Classification

Fibonacci: No

Bell Number: No

Factorial Number: No

Regular Number: No

Perfect Number: No

Special

Kaprekar Constant: No

Munchausen Constant: No

Armstrong Number: No

Kaprekar Number: No

Catalan Number: No

Vampire Number: No

Taxicab Number: No

Super Prime: No

Friedman Number: No

Fermat Number: No

Cullen Number: No

OEIS Sequences

T(n,k) = Number of n X k 0..1 arrays with the number of 1's king-move adjacent to some 0 equal to the number of 0's adjacent to some 1, with top left element zero. A284113

Number of ways to split an integer partition of n into contiguous subsequences with weakly increasing sums. A336136

G.f.: ∏_m>0 1/(1 + x^m + 2·x^2·m + 3·x^3·m). A290395

Numerator of floor(e·10ⁿ)/10ⁿ, where e = exp(1) = A001113. A195604

Number of n X 3 0..1 arrays with the number of 1's king-move adjacent to some 0 equal to the number of 0's adjacent to some 1, with top left element zero. A284108

Number of n X 7 0..1 arrays with the number of 1's king-move adjacent to some 0 equal to the number of 0's adjacent to some 1, with top left element zero. A284112

Sixth Lie-Betti number of a path graph on n vertices. A364946

a(n) is the smallest prime prime(k) such that prime(k-n) and prime(k+n) are balanced primes of order n. A374576

Expansion of (1+3·x+9·x²+12·x³+11·x⁴+3·x⁵+x⁶)/((1-x)²*(1-x²)²*(1-x³)). A55383

Number of divisor chains of length n: permutations s₁,s₂,...,s_n of 1,2,...,n such that for all j=1,2,...,n, s_j divides ∑_i=1..j s_i. A67957