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Atlas › Integer Profiles › Node 3,924,864

3,924,864

27 × 32 × 3407
Abundant Even Composite

3,924,864 factors as 2^7 × 3^2 × 3407. Its 48 positive divisors give a proper-divisor sum of 7,372,656, so this integer is abundant. The Collatz stopping time is 92 steps.

Prime Factor Structure

Factorization String 2^7 × 3^2 × 3407
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 11,297,520
Proper Divisor Sum 7,372,656
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #3924863 ← → #3924871

Radix Representation

Decimal 3924864
Binary 1110111110001110000000 (22 bits)
Octal 0o16761600
Hexadecimal 0x3BE380

Divisor Catalog (48)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 128 144 192 288 384 576 1,152 3,407 6,814 10,221 13,628 20,442 27,256 30,663 40,884 54,512 61,326 81,768 109,024 122,652 163,536 218,048 245,304 327,072 436,096 490,608 654,144 981,216 1,308,288 1,962,432 3,924,864

Collatz Trajectory (92 steps to reach 1)

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

3,924,864 1,962,432 981,216 490,608 245,304 122,652 61,326 30,663 91,990 45,995 137,986 68,993 206,980 103,490 51,745 155,236 77,618 38,809 116,428 58,214 29,107 87,322 43,661 130,984 65,492 32,746 16,373 49,120 24,560 12,280 6,140 3,070 1,535 4,606 2,303 6,910 3,455 10,366 5,183 15,550 7,775 23,326 11,663 34,990 17,495 52,486 26,243 78,730 39,365 118,096 59,048 29,524 14,762 7,381 22,144 11,072 5,536 2,768 1,384 692

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