Properties of the Number 70785

Seventy Thousand Seven Hundred Eighty-Five

Basics

Value: 70784 → 70785 → 70786

Parity: odd

Prime: No

Previous Prime: 70783

Next Prime: 70793

Digit Sum: 27

Digital Root: 9

Palindrome: No

Factorization: 3 ² × 5 × 11 ² × 13

Divisors: 1, 3, 5, 9, 11, 13, 15, 33, 39, 45

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 10001010010000001

Octal: 212201

Duodecimal: 34B69

Hexadecimal: 11481

Square: 5010516225

Square Root: 266.05450569385215

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

Heinz numbers of integer partitions with the same number of even parts, odd parts, even conjugate parts, and odd conjugate parts. A350947

An eight-products triangle sequence of coefficients: T(n,k) = binomial(n,k) * ∏_j=1..7 j!*(n+j)!/((k+j)!*(n-k+j)!). A142468

Antidiagonal-sums of absolute value of the array A377038(n,k) = n-th term of k-th differences of squarefree numbers (A005117). A377040

a(n) = binomial(n+5,5) * binomial(n+5,4)/(n+5). A6857

Ninth column (and diagonal) of Narayana triangle A001263. A134290

Consider the e.g.f. S(x,y) = ∑_n>=0 ∑_k=0..n T(n,k) * x^2·n-2·k+1 * y^2·k / ((2·n-2·k+1)!*(2·k)!) and related functions C(x,y) and D(x,y), as defined in the Formula section. Sequence gives the triangular array of coefficients T(n,k) (n>=0, 0<=k<=n) of S(x,y). A326800

Absolute value of coefficient of term [x^n-4] in characteristic polynomial of maximum matrix A of size n X n, where n >= 4. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n. A112460

Fixed points of A153212: After a(1) = 1, numbers of the form p_i1ⁱ¹ * p_i2^i2-i1 * p_i3^i3-i2 * ... * p_ik^ik-i_k-1, where p_i's are distinct primes present in the prime factorization of n, with i1 < i2 < i3 < ... < ik, and k = A001221(n) and ik = A061395(n). A242421

G.f. A(x) satisfies: A(x) = 1+x + x²*[d/dx A(x)³]. A218223

a(n) = n! * ∑_{k=0..floor(n/3)} (-n/3)^k * binomial(n-2·k,k)/(n-2·k)!. A362304