4,617,585

3² × 5 × 7 × 107 × 137

Starting at 4,617,585, the Collatz iteration reaches 1 after 185 steps. The first transition is 13852756; the starting value is odd with 48 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 5 × 7 × 107 × 137

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 9,300,096

Proper Divisor Sum 4,682,511

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #4617581 ← → #4617601

Radix Representation

Decimal	4617585
Binary	10001100111010101110001 (23 bits)
Octal	0o21472561
Hexadecimal	0x467571

Divisor Catalog (48)

1 3 5 7 9 15 21 35 45 63 105 107 137 315 321 411 535 685 749 959 963 1,233 1,605 2,055 2,247 2,877 3,745 4,795 4,815 6,165 6,741 8,631 11,235 14,385 14,659 33,705 43,155 43,977 73,295 102,613 131,931 219,885 307,839 513,065 659,655 923,517 1,539,195 4,617,585

Collatz Trajectory (185 steps to reach 1)

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

4,617,585 13,852,756 6,926,378 3,463,189 10,389,568 5,194,784 2,597,392 1,298,696 649,348 324,674 162,337 487,012 243,506 121,753 365,260 182,630 91,315 273,946 136,973 410,920 205,460 102,730 51,365 154,096 77,048 38,524 19,262 9,631 28,894 14,447 43,342 21,671 65,014 32,507 97,522 48,761 146,284 73,142 36,571 109,714 54,857 164,572 82,286 41,143 123,430 61,715 185,146 92,573 277,720 138,860 69,430 34,715 104,146 52,073 156,220 78,110 39,055 117,166 58,583 175,750

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