λ
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Atlas › Integer Profiles › Node 99,832,012

99,832,012

22 × 72 × 59 × 89 × 97
Abundant Even Composite

99,832,012 factors as 2^2 × 7^2 × 59 × 89 × 97. Its 72 positive divisors give a proper-divisor sum of 111,318,788, so this integer is abundant. The Collatz stopping time is 187 steps.

Prime Factor Structure

Factorization String 2^2 × 7^2 × 59 × 89 × 97
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 211,150,800
Proper Divisor Sum 111,318,788
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #99832001 ← → #99832021

Radix Representation

Decimal 99832012
Binary 101111100110101000011001100 (27 bits)
Octal 0o574650314
Hexadecimal 0x5F350CC

Divisor Catalog (60 of 72)

1 2 4 7 14 28 49 59 89 97 98 118 178 194 196 236 356 388 413 623 679 826 1,246 1,358 1,652 2,492 2,716 2,891 4,361 4,753 5,251 5,723 5,782 8,633 8,722 9,506 10,502 11,446 11,564 17,266 17,444 19,012 21,004 22,892 34,532 36,757 40,061 60,431 73,514 80,122 120,862 147,028 160,244 241,724 257,299 280,427 423,017 509,347 514,598 560,854

Collatz Trajectory (187 steps to reach 1)

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

99,832,012 49,916,006 24,958,003 74,874,010 37,437,005 112,311,016 56,155,508 28,077,754 14,038,877 42,116,632 21,058,316 10,529,158 5,264,579 15,793,738 7,896,869 23,690,608 11,845,304 5,922,652 2,961,326 1,480,663 4,441,990 2,220,995 6,662,986 3,331,493 9,994,480 4,997,240 2,498,620 1,249,310 624,655 1,873,966 936,983 2,810,950 1,405,475 4,216,426 2,108,213 6,324,640 3,162,320 1,581,160 790,580 395,290 197,645 592,936 296,468 148,234 74,117 222,352 111,176 55,588 27,794 13,897 41,692 20,846 10,423 31,270 15,635 46,906 23,453 70,360 35,180 17,590

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