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Atlas › Integer Profiles › Node 9,734,816

9,734,816

25 × 7 × 13 × 3343
Abundant Even Composite

9,734,816 factors as 2^5 × 7 × 13 × 3343. Its 48 positive divisors give a proper-divisor sum of 13,860,448, so this integer is abundant. The Collatz stopping time is 62 steps.

Prime Factor Structure

Factorization String 2^5 × 7 × 13 × 3343
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 23,595,264
Proper Divisor Sum 13,860,448
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #9734801 ← → #9734827

Radix Representation

Decimal 9734816
Binary 100101001000101010100000 (24 bits)
Octal 0o45105240
Hexadecimal 0x948AA0

Divisor Catalog (48)

1 2 4 7 8 13 14 16 26 28 32 52 56 91 104 112 182 208 224 364 416 728 1,456 2,912 3,343 6,686 13,372 23,401 26,744 43,459 46,802 53,488 86,918 93,604 106,976 173,836 187,208 304,213 347,672 374,416 608,426 695,344 748,832 1,216,852 1,390,688 2,433,704 4,867,408 9,734,816

Collatz Trajectory (62 steps to reach 1)

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

9,734,816 4,867,408 2,433,704 1,216,852 608,426 304,213 912,640 456,320 228,160 114,080 57,040 28,520 14,260 7,130 3,565 10,696 5,348 2,674 1,337 4,012 2,006 1,003 3,010 1,505 4,516 2,258 1,129 3,388 1,694 847 2,542 1,271 3,814 1,907 5,722 2,861 8,584 4,292 2,146 1,073 3,220 1,610 805 2,416 1,208 604 302 151 454 227 682 341 1,024 512 256 128 64 32 16 8

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