2,005,198

2 × 13 × 233 × 331

Starting at 2,005,198, the Collatz iteration reaches 1 after 272 steps. The first transition is 1002599; the starting value is even with 16 positive divisors.

Prime Factor Structure

Factorization String 2 × 13 × 233 × 331

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 3,262,896

Proper Divisor Sum 1,257,698

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #2005193 ← → #2005207

Radix Representation

Decimal	2005198
Binary	111101001100011001110 (21 bits)
Octal	0o7514316
Hexadecimal	0x1E98CE

Divisor Catalog (16)

1 2 13 26 233 331 466 662 3,029 4,303 6,058 8,606 77,123 154,246 1,002,599 2,005,198

Collatz Trajectory (272 steps to reach 1)

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

2,005,198 1,002,599 3,007,798 1,503,899 4,511,698 2,255,849 6,767,548 3,383,774 1,691,887 5,075,662 2,537,831 7,613,494 3,806,747 11,420,242 5,710,121 17,130,364 8,565,182 4,282,591 12,847,774 6,423,887 19,271,662 9,635,831 28,907,494 14,453,747 43,361,242 21,680,621 65,041,864 32,520,932 16,260,466 8,130,233 24,390,700 12,195,350 6,097,675 18,293,026 9,146,513 27,439,540 13,719,770 6,859,885 20,579,656 10,289,828 5,144,914 2,572,457 7,717,372 3,858,686 1,929,343 5,788,030 2,894,015 8,682,046 4,341,023 13,023,070 6,511,535 19,534,606 9,767,303 29,301,910 14,650,955 43,952,866 21,976,433 65,929,300 32,964,650 16,482,325

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