λ
Harmonic Matrix

316,040

23 × 5 × 7901
Abundant Even Composite

316,040 has digital root 5. The neighboring primes are 316037 and 316051; its proper-divisor sum differs from the starting integer by 79,100.

Prime Factor Structure

Factorization String 2^3 × 5 × 7901
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 711,180
Proper Divisor Sum 395,140
Digit Sum / Digital Root 14 (Root: 5)
Adjacent Primes #316037 ← → #316051

Radix Representation

Decimal 316040
Binary 1001101001010001000 (19 bits)
Octal 0o1151210
Hexadecimal 0x4D288

Divisor Catalog (16)

1 2 4 5 8 10 20 40 7,901 15,802 31,604 39,505 63,208 79,010 158,020 316,040

Collatz Trajectory (65 steps to reach 1)

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

316,040 158,020 79,010 39,505 118,516 59,258 29,629 88,888 44,444 22,222 11,111 33,334 16,667 50,002 25,001 75,004 37,502 18,751 56,254 28,127 84,382 42,191 126,574 63,287 189,862 94,931 284,794 142,397 427,192 213,596 106,798 53,399 160,198 80,099 240,298 120,149 360,448 180,224 90,112 45,056 22,528 11,264 5,632 2,816 1,408 704 352 176 88 44 22 11 34 17 52 26 13 40 20 10

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