4,116,125

5³ × 13 × 17 × 149

Starting at 4,116,125, the Collatz iteration reaches 1 after 136 steps. The first transition is 12348376; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 5^3 × 13 × 17 × 149

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 5,896,800

Proper Divisor Sum 1,780,675

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #4116107 ← → #4116127

Radix Representation

Decimal	4116125
Binary	1111101100111010011101 (22 bits)
Octal	0o17547235
Hexadecimal	0x3ECE9D

Divisor Catalog (32)

1 5 13 17 25 65 85 125 149 221 325 425 745 1,105 1,625 1,937 2,125 2,533 3,725 5,525 9,685 12,665 18,625 27,625 32,929 48,425 63,325 164,645 242,125 316,625 823,225 4,116,125

Collatz Trajectory (136 steps to reach 1)

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

4,116,125 12,348,376 6,174,188 3,087,094 1,543,547 4,630,642 2,315,321 6,945,964 3,472,982 1,736,491 5,209,474 2,604,737 7,814,212 3,907,106 1,953,553 5,860,660 2,930,330 1,465,165 4,395,496 2,197,748 1,098,874 549,437 1,648,312 824,156 412,078 206,039 618,118 309,059 927,178 463,589 1,390,768 695,384 347,692 173,846 86,923 260,770 130,385 391,156 195,578 97,789 293,368 146,684 73,342 36,671 110,014 55,007 165,022 82,511 247,534 123,767 371,302 185,651 556,954 278,477 835,432 417,716 208,858 104,429 313,288 156,644

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