λ
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Atlas › Integer Profiles › Node 10,005,330

10,005,330

2 × 3 × 5 × 359 × 929
Abundant Even Composite

10,005,330 factors as 2 × 3 × 5 × 359 × 929. Its 32 positive divisors give a proper-divisor sum of 14,100,270, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 359 × 929
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 24,105,600
Proper Divisor Sum 14,100,270
Digit Sum / Digital Root 12 (Root: 3)
Adjacent Primes #10005329 ← → #10005337

Radix Representation

Decimal 10005330
Binary 100110001010101101010010 (24 bits)
Octal 0o46125522
Hexadecimal 0x98AB52

Divisor Catalog (32)

1 2 3 5 6 10 15 30 359 718 929 1,077 1,795 1,858 2,154 2,787 3,590 4,645 5,385 5,574 9,290 10,770 13,935 27,870 333,511 667,022 1,000,533 1,667,555 2,001,066 3,335,110 5,002,665 10,005,330

Collatz Trajectory (137 steps to reach 1)

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

10,005,330 5,002,665 15,007,996 7,503,998 3,751,999 11,255,998 5,627,999 16,883,998 8,441,999 25,325,998 12,662,999 37,988,998 18,994,499 56,983,498 28,491,749 85,475,248 42,737,624 21,368,812 10,684,406 5,342,203 16,026,610 8,013,305 24,039,916 12,019,958 6,009,979 18,029,938 9,014,969 27,044,908 13,522,454 6,761,227 20,283,682 10,141,841 30,425,524 15,212,762 7,606,381 22,819,144 11,409,572 5,704,786 2,852,393 8,557,180 4,278,590 2,139,295 6,417,886 3,208,943 9,626,830 4,813,415 14,440,246 7,220,123 21,660,370 10,830,185 32,490,556 16,245,278 8,122,639 24,367,918 12,183,959 36,551,878 18,275,939 54,827,818 27,413,909 82,241,728

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