509,823

3² × 37 × 1531

For 509,823, the 12 positive divisors have a total of 756,808. Removing 509,823 leaves 246,985, which gives the deficient classification.

Prime Factor Structure

Factorization String 3^2 × 37 × 1531

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 756,808

Proper Divisor Sum 246,985

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #509801 ← → #509833

Radix Representation

Decimal	509823
Binary	1111100011101111111 (19 bits)
Octal	0o1743577
Hexadecimal	0x7C77F

Divisor Catalog (12)

1 3 9 37 111 333 1,531 4,593 13,779 56,647 169,941 509,823

Collatz Trajectory (363 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

509,823 1,529,470 764,735 2,294,206 1,147,103 3,441,310 1,720,655 5,161,966 2,580,983 7,742,950 3,871,475 11,614,426 5,807,213 17,421,640 8,710,820 4,355,410 2,177,705 6,533,116 3,266,558 1,633,279 4,899,838 2,449,919 7,349,758 3,674,879 11,024,638 5,512,319 16,536,958 8,268,479 24,805,438 12,402,719 37,208,158 18,604,079 55,812,238 27,906,119 83,718,358 41,859,179 125,577,538 62,788,769 188,366,308 94,183,154 47,091,577 141,274,732 70,637,366 35,318,683 105,956,050 52,978,025 158,934,076 79,467,038 39,733,519 119,200,558 59,600,279 178,800,838 89,400,419 268,201,258 134,100,629 402,301,888 201,150,944 100,575,472 50,287,736 25,143,868

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