7,656,507

3² × 101 × 8423

Starting at 7,656,507, the Collatz iteration reaches 1 after 217 steps. The first transition is 22969522; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 101 × 8423

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 11,170,224

Proper Divisor Sum 3,513,717

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7656499 ← → #7656527

Radix Representation

Decimal	7656507
Binary	11101001101010000111011 (23 bits)
Octal	0o35152073
Hexadecimal	0x74D43B

Divisor Catalog (12)

1 3 9 101 303 909 8,423 25,269 75,807 850,723 2,552,169 7,656,507

Collatz Trajectory (217 steps to reach 1)

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

7,656,507 22,969,522 11,484,761 34,454,284 17,227,142 8,613,571 25,840,714 12,920,357 38,761,072 19,380,536 9,690,268 4,845,134 2,422,567 7,267,702 3,633,851 10,901,554 5,450,777 16,352,332 8,176,166 4,088,083 12,264,250 6,132,125 18,396,376 9,198,188 4,599,094 2,299,547 6,898,642 3,449,321 10,347,964 5,173,982 2,586,991 7,760,974 3,880,487 11,641,462 5,820,731 17,462,194 8,731,097 26,193,292 13,096,646 6,548,323 19,644,970 9,822,485 29,467,456 14,733,728 7,366,864 3,683,432 1,841,716 920,858 460,429 1,381,288 690,644 345,322 172,661 517,984 258,992 129,496 64,748 32,374 16,187 48,562

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