Properties of the Number 37193

Thirty-Seven Thousand One Hundred Ninety-Three

Basics

Value: 37192 → 37193 → 37194

Parity: odd

Prime: No

Previous Prime: 37189

Next Prime: 37199

Digit Sum: 23

Digital Root: 5

Palindrome: No

Factorization: 13 × 2861

Divisors: 1, 13, 2861, 37193

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 1001000101001001

Octal: 110511

Duodecimal: 19635

Hexadecimal: 9149

Square: 1383319249

Square Root: 192.85486771144772

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

Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values. A211492

a(n) = ∑_k=1..n floor(n/k); also ∑_k=1..n d(k), where d = number of divisors (A000005); also number of solutions to x·y = z with 1 <= x,y,z <= n. A6218

Sum of totient function: a(n) = ∑_k=1..n φ(k), cf. A000010. A2088

Triangle of Mahonian numbers T(n,k): coefficients in expansion of ∏_i=0..n-1 (1 + x + ... + xⁱ), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index. A8302

Kendall-Mann numbers: the most common number of inversions in a permutation on n letters is floor(n*(n-1)/4); a(n) is the number of permutations with this many inversions. A140

T(n,k) is the coefficient of x^k in ∏_i=1..n (1-xⁱ); triangle T(n,k), n >= 0, 0 <= k <= A000217(n), read by rows. A231599

a(n) is the number of nonzero terms in the expansion of (x-y) * (x²-y²) * (x³-y³) * ... * (xⁿ-yⁿ). A86781

Central nonzero values of A231599. A269298

Number of consonants in n (in French). A37193

a(n) is the smallest positive integer m, with the property that n appears as a coefficient in the polynomial P_m(x) = (x-1)(x²-1)...(x^m-1). A301701