3,412,040

2³ × 5 × 197 × 433

Starting at 3,412,040, the Collatz iteration reaches 1 after 84 steps. The first transition is 1706020; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 197 × 433

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 7,733,880

Proper Divisor Sum 4,321,840

Digit Sum / Digital Root 14 (Root: 5)

Adjacent Primes #3412021 ← → #3412049

Radix Representation

Decimal	3412040
Binary	1101000001000001001000 (22 bits)
Octal	0o15010110
Hexadecimal	0x341048

Divisor Catalog (32)

1 2 4 5 8 10 20 40 197 394 433 788 866 985 1,576 1,732 1,970 2,165 3,464 3,940 4,330 7,880 8,660 17,320 85,301 170,602 341,204 426,505 682,408 853,010 1,706,020 3,412,040

Collatz Trajectory (84 steps to reach 1)

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

3,412,040 1,706,020 853,010 426,505 1,279,516 639,758 319,879 959,638 479,819 1,439,458 719,729 2,159,188 1,079,594 539,797 1,619,392 809,696 404,848 202,424 101,212 50,606 25,303 75,910 37,955 113,866 56,933 170,800 85,400 42,700 21,350 10,675 32,026 16,013 48,040 24,020 12,010 6,005 18,016 9,008 4,504 2,252 1,126 563 1,690 845 2,536 1,268 634 317 952 476 238 119 358 179 538 269 808 404 202 101

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