413,329

7 × 137 × 431

Starting at 413,329, the Collatz iteration reaches 1 after 174 steps. The first transition is 1239988; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 7 × 137 × 431

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 476,928

Proper Divisor Sum 63,599

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #413299 ← → #413353

Radix Representation

Decimal	413329
Binary	1100100111010010001 (19 bits)
Octal	0o1447221
Hexadecimal	0x64E91

Divisor Catalog (8)

1 7 137 431 959 3,017 59,047 413,329

Collatz Trajectory (174 steps to reach 1)

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

413,329 1,239,988 619,994 309,997 929,992 464,996 232,498 116,249 348,748 174,374 87,187 261,562 130,781 392,344 196,172 98,086 49,043 147,130 73,565 220,696 110,348 55,174 27,587 82,762 41,381 124,144 62,072 31,036 15,518 7,759 23,278 11,639 34,918 17,459 52,378 26,189 78,568 39,284 19,642 9,821 29,464 14,732 7,366 3,683 11,050 5,525 16,576 8,288 4,144 2,072 1,036 518 259 778 389 1,168 584 292 146 73

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