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Atlas › Integer Profiles › Node 9,307,746

9,307,746

2 × 32 × 72 × 61 × 173
Abundant Even Composite

9,307,746 factors as 2 × 3^2 × 7^2 × 61 × 173. Its 72 positive divisors give a proper-divisor sum of 14,673,978, so this integer is abundant. The Collatz stopping time is 163 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 7^2 × 61 × 173
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 23,981,724
Proper Divisor Sum 14,673,978
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #9307741 ← → #9307747

Radix Representation

Decimal 9307746
Binary 100011100000011001100010 (24 bits)
Octal 0o43403142
Hexadecimal 0x8E0662

Divisor Catalog (60 of 72)

1 2 3 6 7 9 14 18 21 42 49 61 63 98 122 126 147 173 183 294 346 366 427 441 519 549 854 882 1,038 1,098 1,211 1,281 1,557 2,422 2,562 2,989 3,114 3,633 3,843 5,978 7,266 7,686 8,477 8,967 10,553 10,899 16,954 17,934 21,106 21,798 25,431 26,901 31,659 50,862 53,802 63,318 73,871 76,293 94,977 147,742

Collatz Trajectory (163 steps to reach 1)

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

9,307,746 4,653,873 13,961,620 6,980,810 3,490,405 10,471,216 5,235,608 2,617,804 1,308,902 654,451 1,963,354 981,677 2,945,032 1,472,516 736,258 368,129 1,104,388 552,194 276,097 828,292 414,146 207,073 621,220 310,610 155,305 465,916 232,958 116,479 349,438 174,719 524,158 262,079 786,238 393,119 1,179,358 589,679 1,769,038 884,519 2,653,558 1,326,779 3,980,338 1,990,169 5,970,508 2,985,254 1,492,627 4,477,882 2,238,941 6,716,824 3,358,412 1,679,206 839,603 2,518,810 1,259,405 3,778,216 1,889,108 944,554 472,277 1,416,832 708,416 354,208

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