681,982

2 × 7² × 6959

Starting at 681,982, the Collatz iteration reaches 1 after 229 steps. The first transition is 340991; the starting value is even with 12 positive divisors.

Prime Factor Structure

Factorization String 2 × 7^2 × 6959

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,190,160

Proper Divisor Sum 508,178

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #681979 ← → #681983

Radix Representation

Decimal	681982
Binary	10100110011111111110 (20 bits)
Octal	0o2463776
Hexadecimal	0xA67FE

Divisor Catalog (12)

1 2 7 14 49 98 6,959 13,918 48,713 97,426 340,991 681,982

Collatz Trajectory (229 steps to reach 1)

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

681,982 340,991 1,022,974 511,487 1,534,462 767,231 2,301,694 1,150,847 3,452,542 1,726,271 5,178,814 2,589,407 7,768,222 3,884,111 11,652,334 5,826,167 17,478,502 8,739,251 26,217,754 13,108,877 39,326,632 19,663,316 9,831,658 4,915,829 14,747,488 7,373,744 3,686,872 1,843,436 921,718 460,859 1,382,578 691,289 2,073,868 1,036,934 518,467 1,555,402 777,701 2,333,104 1,166,552 583,276 291,638 145,819 437,458 218,729 656,188 328,094 164,047 492,142 246,071 738,214 369,107 1,107,322 553,661 1,660,984 830,492 415,246 207,623 622,870 311,435 934,306

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