λ
Harmonic Matrix

100,702

2 × 7 × 7193
Deficient Even Composite

100,702 has digital root 1. The neighboring primes are 100699 and 100703; its proper-divisor sum differs from the starting integer by -28,748.

Prime Factor Structure

Factorization String 2 × 7 × 7193
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 172,656
Proper Divisor Sum 71,954
Digit Sum / Digital Root 10 (Root: 1)
Adjacent Primes #100699 ← → #100703

Radix Representation

Decimal 100702
Binary 11000100101011110 (17 bits)
Octal 0o304536
Hexadecimal 0x1895E

Divisor Catalog (8)

1 2 7 14 7,193 14,386 50,351 100,702

Collatz Trajectory (66 steps to reach 1)

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

100,702 50,351 151,054 75,527 226,582 113,291 339,874 169,937 509,812 254,906 127,453 382,360 191,180 95,590 47,795 143,386 71,693 215,080 107,540 53,770 26,885 80,656 40,328 20,164 10,082 5,041 15,124 7,562 3,781 11,344 5,672 2,836 1,418 709 2,128 1,064 532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20

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