827,619

3 × 13 × 21221

Starting at 827,619, the Collatz iteration reaches 1 after 30 steps. The first transition is 2482858; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 3 × 13 × 21221

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 1,188,432

Proper Divisor Sum 360,813

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #827599 ← → #827633

Radix Representation

Decimal	827619
Binary	11001010000011100011 (20 bits)
Octal	0o3120343
Hexadecimal	0xCA0E3

Divisor Catalog (8)

1 3 13 39 21,221 63,663 275,873 827,619

Collatz Trajectory (30 steps to reach 1)

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

827,619 2,482,858 1,241,429 3,724,288 1,862,144 931,072 465,536 232,768 116,384 58,192 29,096 14,548 7,274 3,637 10,912 5,456 2,728 1,364 682 341 1,024 512 256 128 64 32 16 8 4 2 1

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