λ
Harmonic Matrix

3,232,576

26 × 53 × 953
Abundant Even Composite

3,232,576 has digital root 1. The neighboring primes are 3232553 and 3232589; its proper-divisor sum differs from the starting integer by 77,380.

Prime Factor Structure

Factorization String 2^6 × 53 × 953
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 6,542,532
Proper Divisor Sum 3,309,956
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #3232553 ← → #3232589

Radix Representation

Decimal 3232576
Binary 1100010101001101000000 (22 bits)
Octal 0o14251500
Hexadecimal 0x315340

Divisor Catalog (28)

1 2 4 8 16 32 53 64 106 212 424 848 953 1,696 1,906 3,392 3,812 7,624 15,248 30,496 50,509 60,992 101,018 202,036 404,072 808,144 1,616,288 3,232,576

Collatz Trajectory (164 steps to reach 1)

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

3,232,576 1,616,288 808,144 404,072 202,036 101,018 50,509 151,528 75,764 37,882 18,941 56,824 28,412 14,206 7,103 21,310 10,655 31,966 15,983 47,950 23,975 71,926 35,963 107,890 53,945 161,836 80,918 40,459 121,378 60,689 182,068 91,034 45,517 136,552 68,276 34,138 17,069 51,208 25,604 12,802 6,401 19,204 9,602 4,801 14,404 7,202 3,601 10,804 5,402 2,701 8,104 4,052 2,026 1,013 3,040 1,520 760 380 190 95

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