λ
Harmonic Matrix

213,316

22 × 17 × 3137
Deficient Even Composite

213,316 has digital root 7. The neighboring primes are 213307 and 213319; its proper-divisor sum differs from the starting integer by -31,244.

Prime Factor Structure

Factorization String 2^2 × 17 × 3137
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 395,388
Proper Divisor Sum 182,072
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #213307 ← → #213319

Radix Representation

Decimal 213316
Binary 110100000101000100 (18 bits)
Octal 0o640504
Hexadecimal 0x34144

Divisor Catalog (12)

1 2 4 17 34 68 3,137 6,274 12,548 53,329 106,658 213,316

Collatz Trajectory (98 steps to reach 1)

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

213,316 106,658 53,329 159,988 79,994 39,997 119,992 59,996 29,998 14,999 44,998 22,499 67,498 33,749 101,248 50,624 25,312 12,656 6,328 3,164 1,582 791 2,374 1,187 3,562 1,781 5,344 2,672 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822 911 2,734 1,367

More profiles

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