λ
Harmonic Matrix

6,529,164

22 × 3 × 544097
Abundant Even Composite

6,529,164 has digital root 6. The neighboring primes are 6529157 and 6529169; its proper-divisor sum differs from the starting integer by 2,176,416.

Prime Factor Structure

Factorization String 2^2 × 3 × 544097
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 15,234,744
Proper Divisor Sum 8,705,580
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #6529157 ← → #6529169

Radix Representation

Decimal 6529164
Binary 11000111010000010001100 (23 bits)
Octal 0o30720214
Hexadecimal 0x63A08C

Divisor Catalog (12)

1 2 3 4 6 12 544,097 1,088,194 1,632,291 2,176,388 3,264,582 6,529,164

Collatz Trajectory (116 steps to reach 1)

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

6,529,164 3,264,582 1,632,291 4,896,874 2,448,437 7,345,312 3,672,656 1,836,328 918,164 459,082 229,541 688,624 344,312 172,156 86,078 43,039 129,118 64,559 193,678 96,839 290,518 145,259 435,778 217,889 653,668 326,834 163,417 490,252 245,126 122,563 367,690 183,845 551,536 275,768 137,884 68,942 34,471 103,414 51,707 155,122 77,561 232,684 116,342 58,171 174,514 87,257 261,772 130,886 65,443 196,330 98,165 294,496 147,248 73,624 36,812 18,406 9,203 27,610 13,805 41,416

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