557,631

3³ × 19 × 1087

Starting at 557,631, the Collatz iteration reaches 1 after 89 steps. The first transition is 1672894; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 19 × 1087

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 870,400

Proper Divisor Sum 312,769

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #557611 ← → #557633

Radix Representation

Decimal	557631
Binary	10001000001000111111 (20 bits)
Octal	0o2101077
Hexadecimal	0x8823F

Divisor Catalog (16)

1 3 9 19 27 57 171 513 1,087 3,261 9,783 20,653 29,349 61,959 185,877 557,631

Collatz Trajectory (89 steps to reach 1)

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

557,631 1,672,894 836,447 2,509,342 1,254,671 3,764,014 1,882,007 5,646,022 2,823,011 8,469,034 4,234,517 12,703,552 6,351,776 3,175,888 1,587,944 793,972 396,986 198,493 595,480 297,740 148,870 74,435 223,306 111,653 334,960 167,480 83,740 41,870 20,935 62,806 31,403 94,210 47,105 141,316 70,658 35,329 105,988 52,994 26,497 79,492 39,746 19,873 59,620 29,810 14,905 44,716 22,358 11,179 33,538 16,769 50,308 25,154 12,577 37,732 18,866 9,433 28,300 14,150 7,075 21,226

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