7,785,531

3³ × 13 × 41 × 541

Starting at 7,785,531, the Collatz iteration reaches 1 after 323 steps. The first transition is 23356594; the starting value is odd with 32 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 13 × 41 × 541

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 12,747,840

Proper Divisor Sum 4,962,309

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7785521 ← → #7785539

Radix Representation

Decimal	7785531
Binary	11101101100110000111011 (23 bits)
Octal	0o35546073
Hexadecimal	0x76CC3B

Divisor Catalog (32)

1 3 9 13 27 39 41 117 123 351 369 533 541 1,107 1,599 1,623 4,797 4,869 7,033 14,391 14,607 21,099 22,181 63,297 66,543 189,891 199,629 288,353 598,887 865,059 2,595,177 7,785,531

Collatz Trajectory (323 steps to reach 1)

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

7,785,531 23,356,594 11,678,297 35,034,892 17,517,446 8,758,723 26,276,170 13,138,085 39,414,256 19,707,128 9,853,564 4,926,782 2,463,391 7,390,174 3,695,087 11,085,262 5,542,631 16,627,894 8,313,947 24,941,842 12,470,921 37,412,764 18,706,382 9,353,191 28,059,574 14,029,787 42,089,362 21,044,681 63,134,044 31,567,022 15,783,511 47,350,534 23,675,267 71,025,802 35,512,901 106,538,704 53,269,352 26,634,676 13,317,338 6,658,669 19,976,008 9,988,004 4,994,002 2,497,001 7,491,004 3,745,502 1,872,751 5,618,254 2,809,127 8,427,382 4,213,691 12,641,074 6,320,537 18,961,612 9,480,806 4,740,403 14,221,210 7,110,605 21,331,816 10,665,908

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