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Atlas › Integer Profiles › Node 7,705,446

7,705,446

2 × 3 × 72 × 26209
Abundant Even Composite

7,705,446 factors as 2 × 3 × 7^2 × 26209. Its 24 positive divisors give a proper-divisor sum of 10,222,194, so this integer is abundant. The Collatz stopping time is 72 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7^2 × 26209
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 17,927,640
Proper Divisor Sum 10,222,194
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #7705441 ← → #7705519

Radix Representation

Decimal 7705446
Binary 11101011001001101100110 (23 bits)
Octal 0o35311546
Hexadecimal 0x759366

Divisor Catalog (24)

1 2 3 6 7 14 21 42 49 98 147 294 26,209 52,418 78,627 157,254 183,463 366,926 550,389 1,100,778 1,284,241 2,568,482 3,852,723 7,705,446

Collatz Trajectory (72 steps to reach 1)

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

7,705,446 3,852,723 11,558,170 5,779,085 17,337,256 8,668,628 4,334,314 2,167,157 6,501,472 3,250,736 1,625,368 812,684 406,342 203,171 609,514 304,757 914,272 457,136 228,568 114,284 57,142 28,571 85,714 42,857 128,572 64,286 32,143 96,430 48,215 144,646 72,323 216,970 108,485 325,456 162,728 81,364 40,682 20,341 61,024 30,512 15,256 7,628 3,814 1,907 5,722 2,861 8,584 4,292 2,146 1,073 3,220 1,610 805 2,416 1,208 604 302 151 454 227

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