9,732,416

2⁶ × 41 × 3709

Starting at 9,732,416, the Collatz iteration reaches 1 after 114 steps. The first transition is 4866208; the starting value is even with 28 positive divisors.

Prime Factor Structure

Factorization String 2^6 × 41 × 3709

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 28

Divisor Sum (σ) 19,789,140

Proper Divisor Sum 10,056,724

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #9732397 ← → #9732439

Radix Representation

Decimal	9732416
Binary	100101001000000101000000 (24 bits)
Octal	0o45100500
Hexadecimal	0x948140

Divisor Catalog (28)

1 2 4 8 16 32 41 64 82 164 328 656 1,312 2,624 3,709 7,418 14,836 29,672 59,344 118,688 152,069 237,376 304,138 608,276 1,216,552 2,433,104 4,866,208 9,732,416

Collatz Trajectory (114 steps to reach 1)

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

9,732,416 4,866,208 2,433,104 1,216,552 608,276 304,138 152,069 456,208 228,104 114,052 57,026 28,513 85,540 42,770 21,385 64,156 32,078 16,039 48,118 24,059 72,178 36,089 108,268 54,134 27,067 81,202 40,601 121,804 60,902 30,451 91,354 45,677 137,032 68,516 34,258 17,129 51,388 25,694 12,847 38,542 19,271 57,814 28,907 86,722 43,361 130,084 65,042 32,521 97,564 48,782 24,391 73,174 36,587 109,762 54,881 164,644 82,322 41,161 123,484 61,742

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