417,996

2² × 3² × 17 × 683

Starting at 417,996, the Collatz iteration reaches 1 after 280 steps. The first transition is 208998; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 17 × 683

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 1,120,392

Proper Divisor Sum 702,396

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #417983 ← → #417997

Radix Representation

Decimal	417996
Binary	1100110000011001100 (19 bits)
Octal	0o1460314
Hexadecimal	0x660CC

Divisor Catalog (36)

1 2 3 4 6 9 12 17 18 34 36 51 68 102 153 204 306 612 683 1,366 2,049 2,732 4,098 6,147 8,196 11,611 12,294 23,222 24,588 34,833 46,444 69,666 104,499 139,332 208,998 417,996

Collatz Trajectory (280 steps to reach 1)

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

417,996 208,998 104,499 313,498 156,749 470,248 235,124 117,562 58,781 176,344 88,172 44,086 22,043 66,130 33,065 99,196 49,598 24,799 74,398 37,199 111,598 55,799 167,398 83,699 251,098 125,549 376,648 188,324 94,162 47,081 141,244 70,622 35,311 105,934 52,967 158,902 79,451 238,354 119,177 357,532 178,766 89,383 268,150 134,075 402,226 201,113 603,340 301,670 150,835 452,506 226,253 678,760 339,380 169,690 84,845 254,536 127,268 63,634 31,817 95,452

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