1,200,576

2⁶ × 3 × 13² × 37

1,200,576 factors as 2^6 × 3 × 13^2 × 37. Its 84 positive divisors give a proper-divisor sum of 2,332,056, so this integer is abundant. The Collatz stopping time is 235 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 13^2 × 37

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 84

Divisor Sum (σ) 3,532,632

Proper Divisor Sum 2,332,056

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #1200527 ← → #1200581

Radix Representation

Decimal	1200576
Binary	100100101000111000000 (21 bits)
Octal	0o4450700
Hexadecimal	0x1251C0

Divisor Catalog (60 of 84)

1 2 3 4 6 8 12 13 16 24 26 32 37 39 48 52 64 74 78 96 104 111 148 156 169 192 208 222 296 312 338 416 444 481 507 592 624 676 832 888 962 1,014 1,184 1,248 1,352 1,443 1,776 1,924 2,028 2,368 2,496 2,704 2,886 3,552 3,848 4,056 5,408 5,772 6,253 7,104

Collatz Trajectory (235 steps to reach 1)

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

1,200,576 600,288 300,144 150,072 75,036 37,518 18,759 56,278 28,139 84,418 42,209 126,628 63,314 31,657 94,972 47,486 23,743 71,230 35,615 106,846 53,423 160,270 80,135 240,406 120,203 360,610 180,305 540,916 270,458 135,229 405,688 202,844 101,422 50,711 152,134 76,067 228,202 114,101 342,304 171,152 85,576 42,788 21,394 10,697 32,092 16,046 8,023 24,070 12,035 36,106 18,053 54,160 27,080 13,540 6,770 3,385 10,156 5,078 2,539 7,618

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