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Atlas › Integer Profiles › Node 10,092,576

10,092,576

25 × 3 × 13 × 8087
Abundant Even Composite

10,092,576 factors as 2^5 × 3 × 13 × 8087. Its 48 positive divisors give a proper-divisor sum of 18,441,888, so this integer is abundant. The Collatz stopping time is 220 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 13 × 8087
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 28,534,464
Proper Divisor Sum 18,441,888
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #10092571 ← → #10092583

Radix Representation

Decimal 10092576
Binary 100110100000000000100000 (24 bits)
Octal 0o46400040
Hexadecimal 0x9A0020

Divisor Catalog (48)

1 2 3 4 6 8 12 13 16 24 26 32 39 48 52 78 96 104 156 208 312 416 624 1,248 8,087 16,174 24,261 32,348 48,522 64,696 97,044 105,131 129,392 194,088 210,262 258,784 315,393 388,176 420,524 630,786 776,352 841,048 1,261,572 1,682,096 2,523,144 3,364,192 5,046,288 10,092,576

Collatz Trajectory (220 steps to reach 1)

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

10,092,576 5,046,288 2,523,144 1,261,572 630,786 315,393 946,180 473,090 236,545 709,636 354,818 177,409 532,228 266,114 133,057 399,172 199,586 99,793 299,380 149,690 74,845 224,536 112,268 56,134 28,067 84,202 42,101 126,304 63,152 31,576 15,788 7,894 3,947 11,842 5,921 17,764 8,882 4,441 13,324 6,662 3,331 9,994 4,997 14,992 7,496 3,748 1,874 937 2,812 1,406 703 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690

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