7,735,000

2³ × 5⁴ × 7 × 13 × 17

7,735,000 has digital root 4. The neighboring primes are 7734997 and 7735009; its proper-divisor sum differs from the starting integer by 8,147,440.

Prime Factor Structure

Factorization String 2^3 × 5^4 × 7 × 13 × 17

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 160

Divisor Sum (σ) 23,617,440

Proper Divisor Sum 15,882,440

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #7734997 ← → #7735009

Radix Representation

Decimal	7735000
Binary	11101100000011011011000 (23 bits)
Octal	0o35403330
Hexadecimal	0x7606D8

Divisor Catalog (60 of 160)

1 2 4 5 7 8 10 13 14 17 20 25 26 28 34 35 40 50 52 56 65 68 70 85 91 100 104 119 125 130 136 140 170 175 182 200 221 238 250 260 280 325 340 350 364 425 442 455 476 500 520 595 625 650 680 700 728 850 875 884

Collatz Trajectory (124 steps to reach 1)

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

7,735,000 3,867,500 1,933,750 966,875 2,900,626 1,450,313 4,350,940 2,175,470 1,087,735 3,263,206 1,631,603 4,894,810 2,447,405 7,342,216 3,671,108 1,835,554 917,777 2,753,332 1,376,666 688,333 2,065,000 1,032,500 516,250 258,125 774,376 387,188 193,594 96,797 290,392 145,196 72,598 36,299 108,898 54,449 163,348 81,674 40,837 122,512 61,256 30,628 15,314 7,657 22,972 11,486 5,743 17,230 8,615 25,846 12,923 38,770 19,385 58,156 29,078 14,539 43,618 21,809 65,428 32,714 16,357 49,072

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