3,403,820

2² × 5 × 7 × 41 × 593

Starting at 3,403,820, the Collatz iteration reaches 1 after 128 steps. The first transition is 1701910; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 41 × 593

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 8,382,528

Proper Divisor Sum 4,978,708

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #3403789 ← → #3403843

Radix Representation

Decimal	3403820
Binary	1100111111000000101100 (22 bits)
Octal	0o14770054
Hexadecimal	0x33F02C

Divisor Catalog (48)

1 2 4 5 7 10 14 20 28 35 41 70 82 140 164 205 287 410 574 593 820 1,148 1,186 1,435 2,372 2,870 2,965 4,151 5,740 5,930 8,302 11,860 16,604 20,755 24,313 41,510 48,626 83,020 97,252 121,565 170,191 243,130 340,382 486,260 680,764 850,955 1,701,910 3,403,820

Collatz Trajectory (128 steps to reach 1)

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

3,403,820 1,701,910 850,955 2,552,866 1,276,433 3,829,300 1,914,650 957,325 2,871,976 1,435,988 717,994 358,997 1,076,992 538,496 269,248 134,624 67,312 33,656 16,828 8,414 4,207 12,622 6,311 18,934 9,467 28,402 14,201 42,604 21,302 10,651 31,954 15,977 47,932 23,966 11,983 35,950 17,975 53,926 26,963 80,890 40,445 121,336 60,668 30,334 15,167 45,502 22,751 68,254 34,127 102,382 51,191 153,574 76,787 230,362 115,181 345,544 172,772 86,386 43,193 129,580

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