9,782,010

2 × 3² × 5 × 7 × 15527

9,782,010 has digital root 9. The neighboring primes are 9781997 and 9782011; its proper-divisor sum differs from the starting integer by 9,504,396.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 7 × 15527

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 29,068,416

Proper Divisor Sum 19,286,406

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #9781997 ← → #9782011

Radix Representation

Decimal	9782010
Binary	100101010100001011111010 (24 bits)
Octal	0o45241372
Hexadecimal	0x9542FA

Divisor Catalog (48)

1 2 3 5 6 7 9 10 14 15 18 21 30 35 42 45 63 70 90 105 126 210 315 630 15,527 31,054 46,581 77,635 93,162 108,689 139,743 155,270 217,378 232,905 279,486 326,067 465,810 543,445 652,134 698,715 978,201 1,086,890 1,397,430 1,630,335 1,956,402 3,260,670 4,891,005 9,782,010

Collatz Trajectory (176 steps to reach 1)

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

9,782,010 4,891,005 14,673,016 7,336,508 3,668,254 1,834,127 5,502,382 2,751,191 8,253,574 4,126,787 12,380,362 6,190,181 18,570,544 9,285,272 4,642,636 2,321,318 1,160,659 3,481,978 1,740,989 5,222,968 2,611,484 1,305,742 652,871 1,958,614 979,307 2,937,922 1,468,961 4,406,884 2,203,442 1,101,721 3,305,164 1,652,582 826,291 2,478,874 1,239,437 3,718,312 1,859,156 929,578 464,789 1,394,368 697,184 348,592 174,296 87,148 43,574 21,787 65,362 32,681 98,044 49,022 24,511 73,534 36,767 110,302 55,151 165,454 82,727 248,182 124,091 372,274

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