λ
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820,575

32 × 52 × 7 × 521
Abundant Odd Composite

820,575 factors as 3^2 × 5^2 × 7 × 521. Its 36 positive divisors give a proper-divisor sum of 862,353, so this integer is abundant. The Collatz stopping time is 162 steps.

Prime Factor Structure

Factorization String 3^2 × 5^2 × 7 × 521
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 1,682,928
Proper Divisor Sum 862,353
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #820559 ← → #820577

Radix Representation

Decimal 820575
Binary 11001000010101011111 (20 bits)
Octal 0o3102537
Hexadecimal 0xC855F

Divisor Catalog (36)

1 3 5 7 9 15 21 25 35 45 63 75 105 175 225 315 521 525 1,563 1,575 2,605 3,647 4,689 7,815 10,941 13,025 18,235 23,445 32,823 39,075 54,705 91,175 117,225 164,115 273,525 820,575

Collatz Trajectory (162 steps to reach 1)

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

820,575 2,461,726 1,230,863 3,692,590 1,846,295 5,538,886 2,769,443 8,308,330 4,154,165 12,462,496 6,231,248 3,115,624 1,557,812 778,906 389,453 1,168,360 584,180 292,090 146,045 438,136 219,068 109,534 54,767 164,302 82,151 246,454 123,227 369,682 184,841 554,524 277,262 138,631 415,894 207,947 623,842 311,921 935,764 467,882 233,941 701,824 350,912 175,456 87,728 43,864 21,932 10,966 5,483 16,450 8,225 24,676 12,338 6,169 18,508 9,254 4,627 13,882 6,941 20,824 10,412 5,206

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