586,653

3 × 17 × 11503

Starting at 586,653, the Collatz iteration reaches 1 after 97 steps. The first transition is 1759960; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 3 × 17 × 11503

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 828,288

Proper Divisor Sum 241,635

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #586633 ← → #586667

Radix Representation

Decimal	586653
Binary	10001111001110011101 (20 bits)
Octal	0o2171635
Hexadecimal	0x8F39D

Divisor Catalog (8)

1 3 17 51 11,503 34,509 195,551 586,653

Collatz Trajectory (97 steps to reach 1)

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

586,653 1,759,960 879,980 439,990 219,995 659,986 329,993 989,980 494,990 247,495 742,486 371,243 1,113,730 556,865 1,670,596 835,298 417,649 1,252,948 626,474 313,237 939,712 469,856 234,928 117,464 58,732 29,366 14,683 44,050 22,025 66,076 33,038 16,519 49,558 24,779 74,338 37,169 111,508 55,754 27,877 83,632 41,816 20,908 10,454 5,227 15,682 7,841 23,524 11,762 5,881 17,644 8,822 4,411 13,234 6,617 19,852 9,926 4,963 14,890 7,445 22,336

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