7,725,156

2² × 3 × 37 × 127 × 137

Starting at 7,725,156, the Collatz iteration reaches 1 after 217 steps. The first transition is 3862578; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 37 × 127 × 137

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 18,794,496

Proper Divisor Sum 11,069,340

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #7725149 ← → #7725161

Radix Representation

Decimal	7725156
Binary	11101011110000001100100 (23 bits)
Octal	0o35360144
Hexadecimal	0x75E064

Divisor Catalog (48)

1 2 3 4 6 12 37 74 111 127 137 148 222 254 274 381 411 444 508 548 762 822 1,524 1,644 4,699 5,069 9,398 10,138 14,097 15,207 17,399 18,796 20,276 28,194 30,414 34,798 52,197 56,388 60,828 69,596 104,394 208,788 643,763 1,287,526 1,931,289 2,575,052 3,862,578 7,725,156

Collatz Trajectory (217 steps to reach 1)

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

7,725,156 3,862,578 1,931,289 5,793,868 2,896,934 1,448,467 4,345,402 2,172,701 6,518,104 3,259,052 1,629,526 814,763 2,444,290 1,222,145 3,666,436 1,833,218 916,609 2,749,828 1,374,914 687,457 2,062,372 1,031,186 515,593 1,546,780 773,390 386,695 1,160,086 580,043 1,740,130 870,065 2,610,196 1,305,098 652,549 1,957,648 978,824 489,412 244,706 122,353 367,060 183,530 91,765 275,296 137,648 68,824 34,412 17,206 8,603 25,810 12,905 38,716 19,358 9,679 29,038 14,519 43,558 21,779 65,338 32,669 98,008 49,004

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