λ
Harmonic Matrix

1,637,834

2 × 11 × 109 × 683
Deficient Even Composite

1,637,834 has digital root 5. The neighboring primes are 1637813 and 1637851; its proper-divisor sum differs from the starting integer by -567,028.

Prime Factor Structure

Factorization String 2 × 11 × 109 × 683
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 2,708,640
Proper Divisor Sum 1,070,806
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #1637813 ← → #1637851

Radix Representation

Decimal 1637834
Binary 110001111110111001010 (21 bits)
Octal 0o6176712
Hexadecimal 0x18FDCA

Divisor Catalog (16)

1 2 11 22 109 218 683 1,199 1,366 2,398 7,513 15,026 74,447 148,894 818,917 1,637,834

Collatz Trajectory (83 steps to reach 1)

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

1,637,834 818,917 2,456,752 1,228,376 614,188 307,094 153,547 460,642 230,321 690,964 345,482 172,741 518,224 259,112 129,556 64,778 32,389 97,168 48,584 24,292 12,146 6,073 18,220 9,110 4,555 13,666 6,833 20,500 10,250 5,125 15,376 7,688 3,844 1,922 961 2,884 1,442 721 2,164 1,082 541 1,624 812 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49

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