583,752

2³ × 3 × 13 × 1871

Starting at 583,752, the Collatz iteration reaches 1 after 221 steps. The first transition is 291876; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 13 × 1871

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,572,480

Proper Divisor Sum 988,728

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #583733 ← → #583753

Radix Representation

Decimal	583752
Binary	10001110100001001000 (20 bits)
Octal	0o2164110
Hexadecimal	0x8E848

Divisor Catalog (32)

1 2 3 4 6 8 12 13 24 26 39 52 78 104 156 312 1,871 3,742 5,613 7,484 11,226 14,968 22,452 24,323 44,904 48,646 72,969 97,292 145,938 194,584 291,876 583,752

Collatz Trajectory (221 steps to reach 1)

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

583,752 291,876 145,938 72,969 218,908 109,454 54,727 164,182 82,091 246,274 123,137 369,412 184,706 92,353 277,060 138,530 69,265 207,796 103,898 51,949 155,848 77,924 38,962 19,481 58,444 29,222 14,611 43,834 21,917 65,752 32,876 16,438 8,219 24,658 12,329 36,988 18,494 9,247 27,742 13,871 41,614 20,807 62,422 31,211 93,634 46,817 140,452 70,226 35,113 105,340 52,670 26,335 79,006 39,503 118,510 59,255 177,766 88,883 266,650 133,325

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