λ
Harmonic Matrix

655,997

67 × 9791
Deficient Odd Composite

655,997 has digital root 5. The neighboring primes are 655987 and 656023; its proper-divisor sum differs from the starting integer by -646,138.

Prime Factor Structure

Factorization String 67 × 9791
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 665,856
Proper Divisor Sum 9,859
Digit Sum / Digital Root 41 (Root: 5)
Adjacent Primes #655987 ← → #656023

Radix Representation

Decimal 655997
Binary 10100000001001111101 (20 bits)
Octal 0o2401175
Hexadecimal 0xA027D

Divisor Catalog (4)

1 67 9,791 655,997

Collatz Trajectory (110 steps to reach 1)

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

655,997 1,967,992 983,996 491,998 245,999 737,998 368,999 1,106,998 553,499 1,660,498 830,249 2,490,748 1,245,374 622,687 1,868,062 934,031 2,802,094 1,401,047 4,203,142 2,101,571 6,304,714 3,152,357 9,457,072 4,728,536 2,364,268 1,182,134 591,067 1,773,202 886,601 2,659,804 1,329,902 664,951 1,994,854 997,427 2,992,282 1,496,141 4,488,424 2,244,212 1,122,106 561,053 1,683,160 841,580 420,790 210,395 631,186 315,593 946,780 473,390 236,695 710,086 355,043 1,065,130 532,565 1,597,696 798,848 399,424 199,712 99,856 49,928 24,964

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