λ
Harmonic Matrix

310,373

7 × 101 × 439
Deficient Odd Composite

310,373 has digital root 8. The neighboring primes are 310363 and 310379; its proper-divisor sum differs from the starting integer by -261,706.

Prime Factor Structure

Factorization String 7 × 101 × 439
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 359,040
Proper Divisor Sum 48,667
Digit Sum / Digital Root 17 (Root: 8)
Adjacent Primes #310363 ← → #310379

Radix Representation

Decimal 310373
Binary 1001011110001100101 (19 bits)
Octal 0o1136145
Hexadecimal 0x4BC65

Divisor Catalog (8)

1 7 101 439 707 3,073 44,339 310,373

Collatz Trajectory (202 steps to reach 1)

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

310,373 931,120 465,560 232,780 116,390 58,195 174,586 87,293 261,880 130,940 65,470 32,735 98,206 49,103 147,310 73,655 220,966 110,483 331,450 165,725 497,176 248,588 124,294 62,147 186,442 93,221 279,664 139,832 69,916 34,958 17,479 52,438 26,219 78,658 39,329 117,988 58,994 29,497 88,492 44,246 22,123 66,370 33,185 99,556 49,778 24,889 74,668 37,334 18,667 56,002 28,001 84,004 42,002 21,001 63,004 31,502 15,751 47,254 23,627 70,882

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