820,335

3 × 5 × 17 × 3217

820,335 factors as 3 × 5 × 17 × 3217. Its 16 positive divisors give a proper-divisor sum of 569,841, so this integer is deficient. The Collatz stopping time is 87 steps.

Prime Factor Structure

Factorization String 3 × 5 × 17 × 3217

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,390,176

Proper Divisor Sum 569,841

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #820333 ← → #820343

Radix Representation

Decimal	820335
Binary	11001000010001101111 (20 bits)
Octal	0o3102157
Hexadecimal	0xC846F

Divisor Catalog (16)

1 3 5 15 17 51 85 255 3,217 9,651 16,085 48,255 54,689 164,067 273,445 820,335

Collatz Trajectory (87 steps to reach 1)

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

820,335 2,461,006 1,230,503 3,691,510 1,845,755 5,537,266 2,768,633 8,305,900 4,152,950 2,076,475 6,229,426 3,114,713 9,344,140 4,672,070 2,336,035 7,008,106 3,504,053 10,512,160 5,256,080 2,628,040 1,314,020 657,010 328,505 985,516 492,758 246,379 739,138 369,569 1,108,708 554,354 277,177 831,532 415,766 207,883 623,650 311,825 935,476 467,738 233,869 701,608 350,804 175,402 87,701 263,104 131,552 65,776 32,888 16,444 8,222 4,111 12,334 6,167 18,502 9,251 27,754 13,877 41,632 20,816 10,408 5,204

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