586,761

3 × 7 × 27941

Starting at 586,761, the Collatz iteration reaches 1 after 221 steps. The first transition is 1760284; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 3 × 7 × 27941

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 894,144

Proper Divisor Sum 307,383

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #586741 ← → #586769

Radix Representation

Decimal	586761
Binary	10001111010000001001 (20 bits)
Octal	0o2172011
Hexadecimal	0x8F409

Divisor Catalog (8)

1 3 7 21 27,941 83,823 195,587 586,761

Collatz Trajectory (221 steps to reach 1)

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

586,761 1,760,284 880,142 440,071 1,320,214 660,107 1,980,322 990,161 2,970,484 1,485,242 742,621 2,227,864 1,113,932 556,966 278,483 835,450 417,725 1,253,176 626,588 313,294 156,647 469,942 234,971 704,914 352,457 1,057,372 528,686 264,343 793,030 396,515 1,189,546 594,773 1,784,320 892,160 446,080 223,040 111,520 55,760 27,880 13,940 6,970 3,485 10,456 5,228 2,614 1,307 3,922 1,961 5,884 2,942 1,471 4,414 2,207 6,622 3,311 9,934 4,967 14,902 7,451 22,354

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