1,205,200

2⁴ × 5² × 23 × 131

Starting at 1,205,200, the Collatz iteration reaches 1 after 67 steps. The first transition is 602600; the starting value is even with 60 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 23 × 131

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 3,044,448

Proper Divisor Sum 1,839,248

Digit Sum / Digital Root 10 (Root: 1)

Adjacent Primes #1205179 ← → #1205219

Radix Representation

Decimal	1205200
Binary	100100110001111010000 (21 bits)
Octal	0o4461720
Hexadecimal	0x1263D0

Divisor Catalog (60)

1 2 4 5 8 10 16 20 23 25 40 46 50 80 92 100 115 131 184 200 230 262 368 400 460 524 575 655 920 1,048 1,150 1,310 1,840 2,096 2,300 2,620 3,013 3,275 4,600 5,240 6,026 6,550 9,200 10,480 12,052 13,100 15,065 24,104 26,200 30,130 48,208 52,400 60,260 75,325 120,520 150,650 241,040 301,300 602,600 1,205,200

Collatz Trajectory (67 steps to reach 1)

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

1,205,200 602,600 301,300 150,650 75,325 225,976 112,988 56,494 28,247 84,742 42,371 127,114 63,557 190,672 95,336 47,668 23,834 11,917 35,752 17,876 8,938 4,469 13,408 6,704 3,352 1,676 838 419 1,258 629 1,888 944 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40

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