Properties of the Number 58305

Fifty-Eight Thousand Three Hundred Five

Basics

Value: 58304 → 58305 → 58306

Parity: odd

Prime: No

Previous Prime: 58271

Next Prime: 58309

Digit Sum: 21

Digital Root: 3

Palindrome: No

Factorization: 3 × 5 × 13 ² × 23

Divisors: 1, 3, 5, 13, 15, 23, 39, 65, 69, 115

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 1110001111000001

Octal: 161701

Duodecimal: 298A9

Hexadecimal: e3c1

Square: 3399473025

Square Root: 241.46428307308722

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

Smaller of Smith brothers. A50219

Numbers k such that σ(k) = ψ(k) + τ(k)². A390296

Define two triangular arrays by: B(0,0)=C(0,0)=1, B(0,r)=C(0,r)=0 for r>0, C(t,-1)=C(t,0); and for t,r >= 0, B(t+1,r)=C(t,r-1)+2C(t,r)-B(t,r), C(t+1,r)=B(t+1,r)+2B(t+1,r+1)-C(t,r). Sequence gives array B(t,r) read by rows. A177011

E.g.f.: exp(arcsinh(x)*cos(x))=1+x+1/2!*x²-3/3!*x³-15/4!*x⁴-15/5!*x⁵... A12634

cosh(arcsinh(x)*cos(x))=1+1/2!*x²-15/4!*x⁴+225/6!*x⁶-3423/8!*x⁸... A12643

Numerator of H(n), where H(0)=-1/12, H(n) = number of equivalence classes of positive definite quadratic forms a·x²+b·x*y+c·y² with discriminant b²-4ac = -n, counting forms equivalent to x²+y² (resp. x²+x·y+y²) with multiplicity 1/2 (resp. 1/3). A58305