117,649

7⁶

Starting at 117,649, the Collatz iteration reaches 1 after 167 steps. The first transition is 352948; the starting value is odd with 7 positive divisors.

Prime Factor Structure

Factorization String 7^6

Distinct Prime Factors 1

Square Status Yes (√117649 = 343)

Abundance Measure Deficient

Analytical Properties

Total Divisors 7

Divisor Sum (σ) 137,257

Proper Divisor Sum 19,608

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #117643 ← → #117659

Radix Representation

Decimal	117649
Binary	11100101110010001 (17 bits)
Octal	0o345621
Hexadecimal	0x1CB91

Divisor Catalog (7)

1 7 49 343 2,401 16,807 117,649

Collatz Trajectory (167 steps to reach 1)

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

117,649 352,948 176,474 88,237 264,712 132,356 66,178 33,089 99,268 49,634 24,817 74,452 37,226 18,613 55,840 27,920 13,960 6,980 3,490 1,745 5,236 2,618 1,309 3,928 1,964 982 491 1,474 737 2,212 1,106 553 1,660 830 415 1,246 623 1,870 935 2,806 1,403 4,210 2,105 6,316 3,158 1,579 4,738 2,369 7,108 3,554 1,777 5,332 2,666 1,333 4,000 2,000 1,000 500 250 125

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