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Atlas › Integer Profiles › Node 9,902,862

9,902,862

2 × 32 × 29 × 61 × 311
Abundant Even Composite

9,902,862 factors as 2 × 3^2 × 29 × 61 × 311. Its 48 positive divisors give a proper-divisor sum of 12,729,618, so this integer is abundant. The Collatz stopping time is 176 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 29 × 61 × 311
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 22,632,480
Proper Divisor Sum 12,729,618
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #9902861 ← → #9902873

Radix Representation

Decimal 9902862
Binary 100101110001101100001110 (24 bits)
Octal 0o45615416
Hexadecimal 0x971B0E

Divisor Catalog (48)

1 2 3 6 9 18 29 58 61 87 122 174 183 261 311 366 522 549 622 933 1,098 1,769 1,866 2,799 3,538 5,307 5,598 9,019 10,614 15,921 18,038 18,971 27,057 31,842 37,942 54,114 56,913 81,171 113,826 162,342 170,739 341,478 550,159 1,100,318 1,650,477 3,300,954 4,951,431 9,902,862

Collatz Trajectory (176 steps to reach 1)

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

9,902,862 4,951,431 14,854,294 7,427,147 22,281,442 11,140,721 33,422,164 16,711,082 8,355,541 25,066,624 12,533,312 6,266,656 3,133,328 1,566,664 783,332 391,666 195,833 587,500 293,750 146,875 440,626 220,313 660,940 330,470 165,235 495,706 247,853 743,560 371,780 185,890 92,945 278,836 139,418 69,709 209,128 104,564 52,282 26,141 78,424 39,212 19,606 9,803 29,410 14,705 44,116 22,058 11,029 33,088 16,544 8,272 4,136 2,068 1,034 517 1,552 776 388 194 97 292

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