7,820,475

3 × 5² × 13² × 617

Starting at 7,820,475, the Collatz iteration reaches 1 after 248 steps. The first transition is 23461426; the starting value is odd with 36 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 13^2 × 617

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 14,023,656

Proper Divisor Sum 6,203,181

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #7820429 ← → #7820479

Radix Representation

Decimal	7820475
Binary	11101110101010010111011 (23 bits)
Octal	0o35652273
Hexadecimal	0x7754BB

Divisor Catalog (36)

1 3 5 13 15 25 39 65 75 169 195 325 507 617 845 975 1,851 2,535 3,085 4,225 8,021 9,255 12,675 15,425 24,063 40,105 46,275 104,273 120,315 200,525 312,819 521,365 601,575 1,564,095 2,606,825 7,820,475

Collatz Trajectory (248 steps to reach 1)

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

7,820,475 23,461,426 11,730,713 35,192,140 17,596,070 8,798,035 26,394,106 13,197,053 39,591,160 19,795,580 9,897,790 4,948,895 14,846,686 7,423,343 22,270,030 11,135,015 33,405,046 16,702,523 50,107,570 25,053,785 75,161,356 37,580,678 18,790,339 56,371,018 28,185,509 84,556,528 42,278,264 21,139,132 10,569,566 5,284,783 15,854,350 7,927,175 23,781,526 11,890,763 35,672,290 17,836,145 53,508,436 26,754,218 13,377,109 40,131,328 20,065,664 10,032,832 5,016,416 2,508,208 1,254,104 627,052 313,526 156,763 470,290 235,145 705,436 352,718 176,359 529,078 264,539 793,618 396,809 1,190,428 595,214 297,607

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