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Atlas › Integer Profiles › Node 9,729,456

9,729,456

24 × 3 × 11 × 18427
Abundant Even Composite

9,729,456 factors as 2^4 × 3 × 11 × 18427. Its 40 positive divisors give a proper-divisor sum of 17,691,408, so this integer is abundant. The Collatz stopping time is 207 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 11 × 18427
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 27,420,864
Proper Divisor Sum 17,691,408
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #9729427 ← → #9729469

Radix Representation

Decimal 9729456
Binary 100101000111010110110000 (24 bits)
Octal 0o45072660
Hexadecimal 0x9475B0

Divisor Catalog (40)

1 2 3 4 6 8 11 12 16 22 24 33 44 48 66 88 132 176 264 528 18,427 36,854 55,281 73,708 110,562 147,416 202,697 221,124 294,832 405,394 442,248 608,091 810,788 884,496 1,216,182 1,621,576 2,432,364 3,243,152 4,864,728 9,729,456

Collatz Trajectory (207 steps to reach 1)

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

9,729,456 4,864,728 2,432,364 1,216,182 608,091 1,824,274 912,137 2,736,412 1,368,206 684,103 2,052,310 1,026,155 3,078,466 1,539,233 4,617,700 2,308,850 1,154,425 3,463,276 1,731,638 865,819 2,597,458 1,298,729 3,896,188 1,948,094 974,047 2,922,142 1,461,071 4,383,214 2,191,607 6,574,822 3,287,411 9,862,234 4,931,117 14,793,352 7,396,676 3,698,338 1,849,169 5,547,508 2,773,754 1,386,877 4,160,632 2,080,316 1,040,158 520,079 1,560,238 780,119 2,340,358 1,170,179 3,510,538 1,755,269 5,265,808 2,632,904 1,316,452 658,226 329,113 987,340 493,670 246,835 740,506 370,253

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