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Atlas › Integer Profiles › Node 32,005,248

32,005,248

27 × 3 × 11 × 7577
Abundant Even Composite

32,005,248 factors as 2^7 × 3 × 11 × 7577. Its 64 positive divisors give a proper-divisor sum of 60,749,472, so this integer is abundant. The Collatz stopping time is 95 steps.

Prime Factor Structure

Factorization String 2^7 × 3 × 11 × 7577
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 92,754,720
Proper Divisor Sum 60,749,472
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #32005243 ← → #32005249

Radix Representation

Decimal 32005248
Binary 1111010000101110010000000 (25 bits)
Octal 0o172056200
Hexadecimal 0x1E85C80

Divisor Catalog (60 of 64)

1 2 3 4 6 8 11 12 16 22 24 32 33 44 48 64 66 88 96 128 132 176 192 264 352 384 528 704 1,056 1,408 2,112 4,224 7,577 15,154 22,731 30,308 45,462 60,616 83,347 90,924 121,232 166,694 181,848 242,464 250,041 333,388 363,696 484,928 500,082 666,776 727,392 969,856 1,000,164 1,333,552 1,454,784 2,000,328 2,667,104 2,909,568 4,000,656 5,334,208

Collatz Trajectory (95 steps to reach 1)

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

32,005,248 16,002,624 8,001,312 4,000,656 2,000,328 1,000,164 500,082 250,041 750,124 375,062 187,531 562,594 281,297 843,892 421,946 210,973 632,920 316,460 158,230 79,115 237,346 118,673 356,020 178,010 89,005 267,016 133,508 66,754 33,377 100,132 50,066 25,033 75,100 37,550 18,775 56,326 28,163 84,490 42,245 126,736 63,368 31,684 15,842 7,921 23,764 11,882 5,941 17,824 8,912 4,456 2,228 1,114 557 1,672 836 418 209 628 314 157

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