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9,873,006

2 × 3 × 11 × 13 × 37 × 311
Abundant Even Composite

9,873,006 factors as 2 × 3 × 11 × 13 × 37 × 311. Its 64 positive divisors give a proper-divisor sum of 14,028,690, so this integer is abundant. The Collatz stopping time is 313 steps.

Prime Factor Structure

Factorization String 2 × 3 × 11 × 13 × 37 × 311
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 23,901,696
Proper Divisor Sum 14,028,690
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #9872983 ← → #9873011

Radix Representation

Decimal 9873006
Binary 100101101010011001101110 (24 bits)
Octal 0o45523156
Hexadecimal 0x96A66E

Divisor Catalog (60 of 64)

1 2 3 6 11 13 22 26 33 37 39 66 74 78 111 143 222 286 311 407 429 481 622 814 858 933 962 1,221 1,443 1,866 2,442 2,886 3,421 4,043 5,291 6,842 8,086 10,263 10,582 11,507 12,129 15,873 20,526 23,014 24,258 31,746 34,521 44,473 69,042 88,946 126,577 133,419 149,591 253,154 266,838 299,182 379,731 448,773 759,462 897,546

Collatz Trajectory (313 steps to reach 1)

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

9,873,006 4,936,503 14,809,510 7,404,755 22,214,266 11,107,133 33,321,400 16,660,700 8,330,350 4,165,175 12,495,526 6,247,763 18,743,290 9,371,645 28,114,936 14,057,468 7,028,734 3,514,367 10,543,102 5,271,551 15,814,654 7,907,327 23,721,982 11,860,991 35,582,974 17,791,487 53,374,462 26,687,231 80,061,694 40,030,847 120,092,542 60,046,271 180,138,814 90,069,407 270,208,222 135,104,111 405,312,334 202,656,167 607,968,502 303,984,251 911,952,754 455,976,377 1,367,929,132 683,964,566 341,982,283 1,025,946,850 512,973,425 1,538,920,276 769,460,138 384,730,069 1,154,190,208 577,095,104 288,547,552 144,273,776 72,136,888 36,068,444 18,034,222 9,017,111 27,051,334 13,525,667

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