7,729,752

2³ × 3 × 322073

7,729,752 has digital root 3. The neighboring primes are 7729721 and 7729753; its proper-divisor sum differs from the starting integer by 3,864,936.

Prime Factor Structure

Factorization String 2^3 × 3 × 322073

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 19,324,440

Proper Divisor Sum 11,594,688

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #7729721 ← → #7729753

Radix Representation

Decimal	7729752
Binary	11101011111001001011000 (23 bits)
Octal	0o35371130
Hexadecimal	0x75F258

Divisor Catalog (16)

1 2 3 4 6 8 12 24 322,073 644,146 966,219 1,288,292 1,932,438 2,576,584 3,864,876 7,729,752

Collatz Trajectory (217 steps to reach 1)

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

7,729,752 3,864,876 1,932,438 966,219 2,898,658 1,449,329 4,347,988 2,173,994 1,086,997 3,260,992 1,630,496 815,248 407,624 203,812 101,906 50,953 152,860 76,430 38,215 114,646 57,323 171,970 85,985 257,956 128,978 64,489 193,468 96,734 48,367 145,102 72,551 217,654 108,827 326,482 163,241 489,724 244,862 122,431 367,294 183,647 550,942 275,471 826,414 413,207 1,239,622 619,811 1,859,434 929,717 2,789,152 1,394,576 697,288 348,644 174,322 87,161 261,484 130,742 65,371 196,114 98,057 294,172

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