λ
Harmonic Matrix

678,065

5 × 135613
Deficient Odd Composite

678,065 has digital root 5. The neighboring primes are 678061 and 678077; its proper-divisor sum differs from the starting integer by -542,446.

Prime Factor Structure

Factorization String 5 × 135613
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 813,684
Proper Divisor Sum 135,619
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #678061 ← → #678077

Radix Representation

Decimal 678065
Binary 10100101100010110001 (20 bits)
Octal 0o2454261
Hexadecimal 0xA58B1

Divisor Catalog (4)

1 5 135,613 678,065

Collatz Trajectory (229 steps to reach 1)

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

678,065 2,034,196 1,017,098 508,549 1,525,648 762,824 381,412 190,706 95,353 286,060 143,030 71,515 214,546 107,273 321,820 160,910 80,455 241,366 120,683 362,050 181,025 543,076 271,538 135,769 407,308 203,654 101,827 305,482 152,741 458,224 229,112 114,556 57,278 28,639 85,918 42,959 128,878 64,439 193,318 96,659 289,978 144,989 434,968 217,484 108,742 54,371 163,114 81,557 244,672 122,336 61,168 30,584 15,292 7,646 3,823 11,470 5,735 17,206 8,603 25,810

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