λ
Harmonic Matrix

8,528,109

3 × 643 × 4421
Deficient Odd Composite

8,528,109 has digital root 6. The neighboring primes are 8528087 and 8528111; its proper-divisor sum differs from the starting integer by -5,665,146.

Prime Factor Structure

Factorization String 3 × 643 × 4421
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 11,391,072
Proper Divisor Sum 2,862,963
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #8528087 ← → #8528111

Radix Representation

Decimal 8528109
Binary 100000100010000011101101 (24 bits)
Octal 0o40420355
Hexadecimal 0x8220ED

Divisor Catalog (8)

1 3 643 1,929 4,421 13,263 2,842,703 8,528,109

Collatz Trajectory (150 steps to reach 1)

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

8,528,109 25,584,328 12,792,164 6,396,082 3,198,041 9,594,124 4,797,062 2,398,531 7,195,594 3,597,797 10,793,392 5,396,696 2,698,348 1,349,174 674,587 2,023,762 1,011,881 3,035,644 1,517,822 758,911 2,276,734 1,138,367 3,415,102 1,707,551 5,122,654 2,561,327 7,683,982 3,841,991 11,525,974 5,762,987 17,288,962 8,644,481 25,933,444 12,966,722 6,483,361 19,450,084 9,725,042 4,862,521 14,587,564 7,293,782 3,646,891 10,940,674 5,470,337 16,411,012 8,205,506 4,102,753 12,308,260 6,154,130 3,077,065 9,231,196 4,615,598 2,307,799 6,923,398 3,461,699 10,385,098 5,192,549 15,577,648 7,788,824 3,894,412 1,947,206

More profiles

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