7,822,762

2 × 37 × 61 × 1733

Starting at 7,822,762, the Collatz iteration reaches 1 after 186 steps. The first transition is 3911381; the starting value is even with 16 positive divisors.

Prime Factor Structure

Factorization String 2 × 37 × 61 × 1733

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 12,255,912

Proper Divisor Sum 4,433,150

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #7822741 ← → #7822769

Radix Representation

Decimal	7822762
Binary	11101110101110110101010 (23 bits)
Octal	0o35656652
Hexadecimal	0x775DAA

Divisor Catalog (16)

1 2 37 61 74 122 1,733 2,257 3,466 4,514 64,121 105,713 128,242 211,426 3,911,381 7,822,762

Collatz Trajectory (186 steps to reach 1)

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

7,822,762 3,911,381 11,734,144 5,867,072 2,933,536 1,466,768 733,384 366,692 183,346 91,673 275,020 137,510 68,755 206,266 103,133 309,400 154,700 77,350 38,675 116,026 58,013 174,040 87,020 43,510 21,755 65,266 32,633 97,900 48,950 24,475 73,426 36,713 110,140 55,070 27,535 82,606 41,303 123,910 61,955 185,866 92,933 278,800 139,400 69,700 34,850 17,425 52,276 26,138 13,069 39,208 19,604 9,802 4,901 14,704 7,352 3,676 1,838 919 2,758 1,379

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