λ
Harmonic Matrix

8,688,155

5 × 7 × 37 × 6709
Deficient Odd Composite

8,688,155 has digital root 5. The neighboring primes are 8688143 and 8688157; its proper-divisor sum differs from the starting integer by -5,137,270.

Prime Factor Structure

Factorization String 5 × 7 × 37 × 6709
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 12,239,040
Proper Divisor Sum 3,550,885
Digit Sum / Digital Root 41 (Root: 5)
Adjacent Primes #8688143 ← → #8688157

Radix Representation

Decimal 8688155
Binary 100001001001001000011011 (24 bits)
Octal 0o41111033
Hexadecimal 0x84921B

Divisor Catalog (16)

1 5 7 35 37 185 259 1,295 6,709 33,545 46,963 234,815 248,233 1,241,165 1,737,631 8,688,155

Collatz Trajectory (181 steps to reach 1)

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

8,688,155 26,064,466 13,032,233 39,096,700 19,548,350 9,774,175 29,322,526 14,661,263 43,983,790 21,991,895 65,975,686 32,987,843 98,963,530 49,481,765 148,445,296 74,222,648 37,111,324 18,555,662 9,277,831 27,833,494 13,916,747 41,750,242 20,875,121 62,625,364 31,312,682 15,656,341 46,969,024 23,484,512 11,742,256 5,871,128 2,935,564 1,467,782 733,891 2,201,674 1,100,837 3,302,512 1,651,256 825,628 412,814 206,407 619,222 309,611 928,834 464,417 1,393,252 696,626 348,313 1,044,940 522,470 261,235 783,706 391,853 1,175,560 587,780 293,890 146,945 440,836 220,418 110,209 330,628

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